Analysis
Grenzwerte, Ableitungen, Optimierung und Funktionsverhalten.
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select all the correct answers. graph the following function. \\( f(x) …
- When x = -1, f(x) = 0. - As x approaches positive infinity, f(x) approaches positive infinity. - As x approaches negative infinity, f(x) approaches positive infinity.
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select all the correct answers. determine the solutions for the system …
$(2, \frac{5}{4})$, $(-3, \frac{45}{4})$
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identify the transformations made on f(x) = 10^x to create the graph of…
The correct option is the orange one: reflection over x - axis, vertical compression by 2/3, right 8
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identify the transformations made on f(x) = e^x to create the graph of …
The correct option is the first one (the yellow - colored card): vertical compression by a factor of \( \frac{1}{2} \), reflection over \( x \)-axis, left 6, up 4.
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independent practice: subtracting decimals to thousandths name no regro…
For problem 1, the result is \( 2.112 \) (If you want solutions for other problems, you can follow the same steps: align the decimal points and subtract each column from right to …
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adding decimals worksheet 94.6 + 36.8 35.75 + 387.8 88.55 + 25.8 731.89…
To solve these decimal addition problems, we follow the standard procedure of aligning the decimal points and adding the numbers column by column, carrying over when necessary. Le…
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which graphs has a negative slope? select all correct options
The graphs with negative slopes are the blue - colored graph and the light blue - colored graph (select the blue and light blue options).
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graphing an equation in slope-intercept form graph: $y = \\frac{3}{4}x …
To graph \( y=\frac{3}{4}x + 5 \): 1. Plot the y - intercept \( (0,5) \) (since \( b = 5 \) in \( y=mx + b \)). 2. Use the slope \( \frac{3}{4} \) to find other points (e.g., from…
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2. $19 + 16 = ____________$ 3. $37 + 2 \\times 6 = ____________$ 4. wri…
35 ### Question 3
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question 2 of 5 according to the drafters of the declaration of indepen…
D. By making it hard for people to become citizens
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1. $1 \\times 3 = $ \t $40 \\div 4 = $ $2 \\times 3 = $ \t $4 \\div 4 =…
| \(1\times3 =\) 3 | \(40\div4 =\) 10 | | \(2\times3 =\) 6 | \(4\div4 =\) 1 | | \(3\times3 =\) 9 | \(36\div4 =\) 9 | | \(4\times3 =\) 12 | \(8\div4 =\) 2 | | \(5\times3 =\) 15 | \…
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together, generous financial support and an under- standing on our part…
B. Rationing (assuming the options are labeled as such; from the given options, the correct one is the "Rationing" option)
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11. add. $2\\frac{9}{10}+\\frac{-1}{2}=\\square$ 12. subtract. $\\frac{…
11. $1\frac{9}{10}$ (or $\frac{19}{10}$, or 1.9) 12. $-6\frac{3}{4}$ (or $\frac{-27}{4}$, or -6.75) 13. $2.35$ 14. $0.75$ 15. $-12.3$ 16. $-5.1$
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6. add. \\(\frac{1}{2} + 8\frac{4}{5} = \\) 7. add. \\(-3 + -3.5 = \\) …
6. $9\frac{3}{10}$ 7. $-6.5$ 8. $\frac{4}{5}$ 9. $-\frac{8}{5}$ or $-1\frac{3}{5}$ 10. $\frac{7}{10}$
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17. add. \\(\frac{3}{4} + -6\frac{1}{2} = square\\) 18. add. \\(6\frac{…
17. $-5\frac{3}{4}$ (or $-\frac{23}{4}$) 18. $9\frac{3}{5}$ (or $\frac{48}{5}$) 19. $-8\frac{7}{10}$ (or $-\frac{87}{10}$) 20. $10\frac{1}{4}$ (or $\frac{41}{4}$)
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y = \frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0, -7) \). 2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0, -7) \), move up 4, rig…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point: from \( (0,-7) \), move 5 units right and 4…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point: from \( (0,-7) \), move up 4 and right 5 to…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7) \), move 5 units right…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7) \), move 4 up and 5 ri…
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graph $y = \\frac{4}{5}x - 7$.
To graph \(y = \frac{4}{5}x-7\): 1. Plot the y - intercept \((0,-7)\). 2. Use the slope \(\frac{4}{5}\) to find another point (e.g., from \((0,-7)\), move up 4 and right 5 to get …
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \), plot the y - intercept \( (0,-7) \) and the point \( (5,-3) \) (found using the slope \( \frac{4}{5} \)) and draw a line through them.
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7) \), move up 4 and right 5…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \), plot the y - intercept \( (0,-7) \) and the point \( (5,-3) \) (found using the slope \( \frac{4}{5} \)) and draw a line through these points.
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graph $y = \\frac{4}{5}x - 7$.
To graph \(y=\frac{4}{5}x - 7\): 1. Plot the y - intercept \((0,-7)\) on the y - axis. 2. Use the slope \(\frac{4}{5}\) (rise = 4, run = 5) to find another point. From \((0,-7)\),…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point: from \( (0,-7) \), move up 4 units and righ…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7\): 1. Plot the y - intercept at \((0,-7)\). 2. Use the slope \(\frac{4}{5}\) to find another point (e.g., from \((0,-7)\), move 5 units right and 4 …
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0, - 7) \). 2. Use the slope \( \frac{4}{5} \) to find another point: from \( (0,-7) \), move 5 units right and…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7) \), move up 4 and righ…
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((10 - 6 + 5) ÷ 9) × 2
$2$
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graph $y = \\frac{4}{5}x - 7$.
The given graph is incorrect. To graph \( y=\frac{4}{5}x - 7 \), plot the y - intercept \( (0,-7) \) and use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find additional points (e.g., from \( (0,-7) \), moving 5 units ri…
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graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \), plot the y - intercept \( (0,-7) \), then use the slope \( \frac{4}{5} \) to find another point (e.g., \( (5,-3) \)) and draw a straight line th…
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in each equation, the ? represents an operation. which operation makes …
a. Division ($\div$) b. Division ($\div$) c. Addition ($+$) d. Subtraction ($-$) e. Addition ($+$) f. Multiplication ($\times$)
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look at this graph: what is the minimum value of this function?
-10
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graph $y = \\frac{4}{5}x - 7$.
The graph is a straight line passing through the points $(0, -7)$ and $(5, -3)$, following the equation $y = \frac{4}{5}x - 7$.
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graph $y = \\frac{4}{5}x - 7$.
The graph is a straight line passing through the points $(0, -7)$ and $(5, -3)$, following the equation $y=\frac{4}{5}x-7$.
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graph $y = \\frac{4}{5}x - 7$.
The line passes through points $(0, -7)$ and $(5, -3)$, extending infinitely in both directions on the coordinate plane.
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graph $y = \\frac{4}{5}x - 7$.
The line passes through points $(0, -7)$ and $(5, -3)$, extending infinitely in both directions on the coordinate plane.
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graph $y = \\frac{4}{5}x - 7$.
The line passes through points $(0, -7)$ and $(5, -3)$, and extends infinitely in both directions on the coordinate plane.
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((10 - 6 + 5) ÷ 9) × 2
\(2\)
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14. consider the function $y = 0.54(0.3)^x$. 14a identify what type of …
The rate of decay is \( 0.7 \) (or \( 70\% \)).
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14. consider the function $y = 0.54(0.3)^x$. 14a identify what type of …
B. Exponential decay
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13. consider the curve $y = 5(2^x)$. 13d what is the range of the funct…
\(\infty\) (the option with \(\infty\))
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13. consider the curve $y = 5(2^x)$. 13d what is the range of the funct…
\(y > 0\)
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13. consider the curve $y = 5(2^x)$. 13b can the function value ever be…
all real \( x \)
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13. consider the curve $y = 5(2^x)$. 13a determine the $y$-intercept of…
B. No
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13. consider the curve $y = 5(2^x)$. 13a determine the $y$-intercept of…
\(5\)
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12b as the value of x gets large in the negative direction, what do the…
B. A horizontal asymptote of the curve.
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consider the graph of the equation $y = 2^x$. 12a what can we say about…
The values of \( y \) approach \( 0 \) but never quite reach it. So the correct option is the one with \( 0 \) (assuming the options are labeled with \( 0 \), \( -2 \), \( 2 \), a…
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12 consider the graph of the equation $y = 2^x$. what can we say about …
The \( y \)-value of every point on the graph is positive.
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11. fill in the missing coordinate in each ordered pair so that the pai…
5
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evaluate the expression. -0.8 + 0.7 - 7 × -0.1 write your answer as an …
\(0.6\)
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evaluate the expression. $-\frac{2}{5} \\times \frac{3}{4} + \frac{3}{5…
\(-\frac{21}{10}\)
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evaluate the expression. \\(\frac{3}{4} \times \frac{1}{2} div left( \f…
$\frac{5}{2}$ (or $2\frac{1}{2}$)
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match each polynomial function to its graph. \\( f(x) = -x^3 - 2x^2 - x…
- \( f(x)=-x^{3}-2x^{2}-x - 3 \) matches the fourth graph (right - bottom). - \( g(x)=3x^{4}-3x^{3}-9x^{2}+6x + 3 \) matches the second graph (right - top). - \( h(x)=x^{3}-2x^{2}…
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find the vertical asymptotes, if any, of the graph of the rational func…
None of the provided options match the correct result. The correct vertical asymptote is $x=0$. *Note: If forced to select from the given options, there is no correct choice. The …
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examples 1-2 complete parts a–c for each quadratic function. a. find th…
Let's solve problem 19: \( f(x) = x^2 - 3x - 10 \) for part a (find y - intercept, axis of symmetry, x - coordinate of vertex), part b (table of values including vertex), and part…
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if $g(x) = 4x^{4} - 23x^{3} + 10x^{2} + 25x$, use synthetic division to…
\( 0 \)
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which graph represents a function with an initial value of \\(\\frac{1}…
The second graph (the one with the curve passing through $(0, \frac{1}{2})$)
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which graph represents a function with a growth factor of 5?
The third graph (left-to-right, the one with the steepest vertical rise from the x-axis)
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vertical stretches and shrinks of exponential functions which graph rep…
The third graph (the lower of the two upward-sloping exponential curves, labeled with the top-most of the two bottom option markers)
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if $p(x) = 3x^3 + 7x^2 - 5x - 25$, use synthetic division to find $p(-3…
\( -28 \)
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if $f(x) = 9x^3 + 6x^2 + 33$, use synthetic division to find $f(-1)$. s…
\( 30 \)
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which exponential function is represented by the graph? options: $f(x) …
$f(x)=3(2^x)$
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11. fill in the missing coordinate in each ordered pair so that the pai…
-2
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11. fill in the missing coordinate in each ordered pair so that the pai…
\(-81\)
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if $g(v) = 2v^{4} + 16v^{3} + 25v^{2} - 33v - 20$, use synthetic divisi…
\( 0 \)
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10. consider the function $f(x)=|x + 5|$. 10a does the graph of the fun…
\((-5, 0)\)
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if $f(x) = 38x^2 - 30x + 14$, use synthetic division to find $f(1)$.
22
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below is the graph of $y = |x|$. translate it to make it the graph of $…
Translate the graph of \( y = |x| \) 3 units to the right and 2 units up.
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graph this line: y - 7 = -4(x - 1) click to select points on the grap
To graph the line \( y - 7=-4(x - 1) \): 1. Identify the point \( (1,7) \) from the point - slope form. 2. Use the slope \( m=-4 \) to find additional points (e.g., \( (2,3) \) or…
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what is the slope of this line? (-3, 4) (3, -4)
\(-\frac{4}{3}\)
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8. a seat’s position on a ferris wheel can be modelled by the function …
8. $5.6$ metres 9. a) 2.0 metres. This is the midline of the sinusoidal graph, found by $\frac{2.8 + 1.2}{2} = 2.0$, which is the stable depth without waves. b) 0.8 metres. Calcul…
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refer to the functions r, p, and q. find the function (p·q)(x) and writ…
\(x(x + 5)\sqrt{9 - x}\) (or \((x^{2}+5x)\sqrt{9 - x}\))
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given the functions: $f(x)=7x$ $g(x)=|x - 2|$ $h(x)=\frac{1}{x - 4}$ ev…
\(-1\)
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find $(f + g)(x)$ and identify the graph of $f + g$. $f(x) = x^2$ and $…
\( x^{2}+3 \)
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express the set using the roster method. {x|x is a lowercase letter of …
B. {d, e, f, g}
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use transformations to graph the function.\\( p(x)=sqrt{-x + 2} \\)
To graph \( p(x)=\sqrt{-x + 2} \) using transformations: 1. **Start with the parent function** \( y = \sqrt{x} \) (domain \( x\geq0 \), vertex \( (0,0) \), increasing to the right…
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use transformations to graph the function. \\( r(x) = \\sqrt{-x + 4} \\)
To graph \( r(x) = \sqrt{-x + 4} \) using transformations: 1. **Parent Function**: Start with \( y = \sqrt{x} \) (domain \( x \geq 0 \), starts at \( (0, 0) \), increases). 2. **H…
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find the lines slope and a point on the line. $y + 4 = -\\frac{2}{3}(x …
slope: $-\frac{2}{3}$ point on the line: $(4, -4)$
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the graph shows ( g(x) ), which is a translation of ( f(x) = x^2 ). wri…
$g(x)=(x+4)^2+2$
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find the equation of the square root function described contextually - …
$f(x) = -9\sqrt{x+4} + 8$
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yesterday - answer the questions below. 6. which statement would most l…
B. "We must limit immigration to protect American jobs." ### Question 7
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graph the following equation in a rectangular coordinate system. y = -5…
A horizontal straight line passing through the point $(0, -5)$ (parallel to the x-axis, with all points on the line having a y-coordinate of $-5$).
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lesson 1.2 homework complete problems 3, 4, 6, 8, 9, 11, 13, 15, 18, 21…
\( f(-3) = -16 \) ### Problem 4: Evaluate \( f(-2) \)
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example 4) solve $-\frac{1}{3}(-x + 9)=\frac{2}{3}x - 2$ by graphing. e…
$x=5$
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write the square root function that corresponds to the points shown on …
$f(x) = 1\sqrt{-1(x - 4)} + 5$ (or formatted as $f(x)=\sqrt{4-x}+5$)
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example 3) solve $-2x + 6 = -2(x - 3)$ by graphing. equation 1: $square…
Equation 1: The y - intercept is \( 6 \), The slope is \( - 2 \) Equation 2: The y - intercept is \( 6 \), The slope is \( - 2 \) The two equations represent the same line, so the…
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visit www.bigideasmathvideos.com to watch the flipped video instruction…
\( f(-1)=-3 \) ### 2. Evaluate \( f(1) \)
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try this video for extra example evaluate the function. 1. $f(-1)$
To evaluate \( f(-1) \), we need the definition of the function \( f(x) \). Since the function's formula is not provided in the image, we can't proceed with the calculation. Pleas…
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determine whether the following statements are true and give an explana…
A. True. Since the graph of \( f \) is symmetric about the \( y \)-axis, the surface area generated when the graph of \( f \) on \([-a,a]\) is revolved around the \( x \)-axis is …
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23. \\(\frac{sqrt3{54}}{sqrt3{2}}\\)\ 24. \\(\frac{sqrt3{350}}{sqrt3{50…
$3$ ### Problem 24: $\boldsymbol{\frac{\sqrt[3]{350}}{\sqrt[3]{500}}}$
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name write the answer for each problem. if you don’t know how to work t…
1. $60 \div 5 = 12$ 2. $-77 + (-18) + (-33) = -128$ 3. $\frac{18}{10} \div \frac{9}{10} = 2$ 4. $2.14 \times 3.02 = 6.4628$ 5. $746 \times 230 = 171580$ 6. $\frac{5}{4} \div \frac…
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determine the general anti - derivative for the following function. use…
$e^x + \frac{x^6}{6} + C$
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express the limit as a definite integral. \\(\\lim_{n\\to\\infty} \\fra…
$\int_{0}^{1} \frac{9}{1+x^6} dx$
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21. -/4 points if ( m leq f(x) leq m ) for ( a leq x leq b ), where ( m…
smaller value: $0$ larger value: $\frac{12}{e}$ (or approximately $4.41$)
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3 f(x) = 3x⁴ + 2x² + x + 7 orange as x → -∞, f(x) → ∞ as x → ∞, f(x) → …
ORANGE: as $x \to -\infty, f(x) \to \infty$; as $x \to \infty, f(x) \to \infty$
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he corresponding number on the picture. d $f(x) = -2x^5 - 3x^3 + 2x - 8…
The function \( f(x)=-2x^5 - 3x^3+2x - 8 \) has the end - behavior that matches the GREEN category. So the answer is GREEN.
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polynomial e find your answer from the choices and color the 1 white as…
Yellow (with the description "as \(x ightarrow-\infty,f(x) ightarrow-\infty\); as \(x ightarrow\infty,f(x) ightarrow\infty\)")