Analysis
Grenzwerte, Ableitungen, Optimierung und Funktionsverhalten.
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f(x) = x² - x - 1 over which interval does f have an average rate of ch…
A. \(-1 \leq x \leq 2\)
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f(x) = x² - x - 1 over which interval does f have an average rate of ch…
A. \(-1 \leq x \leq 2\)
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question 3 (1 point) compare the graph to the absolute value parent fun…
a. Reflected over the x - axis, c. Horizontal Shift Right, e. Vertical Shift Down, f. Graph is Narrower
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compare the graph to the absolute value parent function ($y = |x|$). se…
b. Horizontal Shift Left, e. Vertical Shift Down, f. Graph is Narrower
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evaluate the function for the given value. f(x) = 2x - 4 for x = -2 f(-…
$-8$
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solve the equation. \\(\\frac{4}{5} \\div \\frac{3}{4} = \\square\\) su…
$\frac{16}{15}$ or $1\frac{1}{15}$
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solve the equation. \\(\\frac{4}{5} \\div \\frac{3}{4} = \\square\\) su…
$\frac{16}{15}$ or $1\frac{1}{15}$
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4 find the slope m of the line in the graph below. m = 4
\(4\)
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which of the relationships below represents a function with the same sl…
A. | $x$ | $y$ | |-----|-----| | $-6$ | $12$ | | $-4$ | $9$ | | $-2$ | $6$ | | $0$ | $3$ |
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10. y = -4 slope (m) = y-intercept (b) = 11. y + x = 3 slope (m) = y-in…
slope (\( m \)) = \( 0 \) y - intercept (\( b \)) = \( -4 \) ### Problem 11: \( y + x=3 \) (rewrite as \( y=-x + 3 \))
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the table below represents a linear function. identify the slope of the…
4
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6. which points are on the graph of the function rule $f(x) = 10 - 4x$?…
\((-2, 18), (0, 10), (2, 2)\) (la cuarta opción)
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f(x) = x⁴ + 4x² + 3; g(x) = 3x⁴ + 12x³ + 18x² + 12x + 3
For \( f(x) \), factored form is \( \boldsymbol{(x^2 + 1)(x^2 + 3)} \); for \( g(x) \), factored form is \( \boldsymbol{3(x + 1)^4} \). If analyzing the graph, \( f(x) \) is symme…
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3 use numbers from the box to complete the equation a. $0.8 \\times 0.8…
\(0.64\) (if box has 0.64, else 0.6 as a typo) ### Part b
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solve the following system of inequalities graphically on the set of ax…
A point in the solution set is $(0, 0)$ (other valid points include $(2, 1)$, $(-1, 0)$, etc.)
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question 7 (mandatory) (1 point) determine the roots of $3.3x^2 + 1.9x …
d) -1.19 and 0.61
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imagine 6 in your head double it add 3 write the tens digit. a imagine …
1 ### Second Box (B and C)
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6. * which graph represents the system of equations? ( y = \frac{2}{3}x…
C
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question 16 (1 point) compare the equation to the absolute value parent…
d. Vertical Shift Up, g. Graph is Wider
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question 15 (1 point) compare the equation to the absolute value parent…
b. Horizontal Shift Left f. Graph is Narrower
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question 13 (1 point) compare the equation to the absolute value parent…
a. Reflected over the x - axis
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compare the equation to the absolute value parent function ($y = |x|$).…
e. Vertical Shift Down
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3\\overline{) 36}
The result of \( 36 \div 3 \) is 12.
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question 11 (1 point) compare the equation to the absolute value parent…
b. Horizontal Shift Left
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which graph represents the function $f(x) = -(x - 3)^2 + 1$? a) graph w…
b) The graph with vertex at (3, 1) and opening downward.
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question 9 (1 point) compare the graph to the absolute value parent fun…
a. Reflected over the x - axis
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compare the graph to the absolute value parent function ($y = |x|$). se…
e. Vertical Shift Down
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20 ) 6801 divide and write remainder.
When dividing 6801 by 200 (assuming the smudged digit is 0), the quotient is 34 and the remainder is 1.
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compare the graph to the absolute value parent function ($y = |x|$). se…
b. Horizontal Shift Left, d. Vertical Shift Up, f. Graph is Narrower
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question 2 (mandatory) (1 point) if $f(2) = 2$, what is $3f(2)$? \\bigc…
d) 6
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which graph represents the system of equations? $y = \\frac{2}{5} x +1$…
C ### Question 7 (Solving the System of Equations)
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solve $6.13 \\div 5$ using the division algorithm. divide 6 ones by 5. …
The first box (the product) is \(5\) and the second box (the remainder) is \(1\). So filling in the boxes, we have \(-\boxed{5}\) and then \(\boxed{1}\) below it.
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the graph of $y = |x|$ is reflected across the $x$-axis and then scaled…
D. \( y = -\frac{3}{8}\vert x\vert \)
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compare the graph to the absolute value parent function ($y = |x|$). se…
a. Reflected over the x - axis, c. Horizontal Shift Right, f. Graph is Narrower
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which equation is perpendicular to $y = 4x - 6$ and passes through poin…
B. $y = -\frac{1}{4}x + 14$
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Question was provided via image upload.
$\frac{7}{12}$
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Question was provided via image upload.
$\frac{1}{3}$
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compare the graph to the absolute value parent function ($y = |x|$). se…
c. Horizontal Shift Right, d. Vertical Shift Up
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question 4 (1 point) compare the graph to the absolute value parent fun…
b. Horizontal Shift Left, e. Vertical Shift Down
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over which interval does f have an average rate of change of zero? choo…
C. \( -3 \leq x \leq -2 \)
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question 3 (1 point) compare the graph to the absolute value parent fun…
a. Reflected over the x - axis, c. Horizontal Shift Right, e. Vertical Shift Down, f. Graph is Narrower
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subtract. \\(\\frac{5}{6} - \\frac{1}{2} = \\square\\) use the model to…
$\frac{1}{3}$
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compare the graph to the absolute value parent function ($y = |x|$). se…
b. Horizontal Shift Left, e. Vertical Shift Down, f. Graph is Narrower
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evaluate the function for the given value. f(x) = 2x - 4 for x = -2 f(-…
$-8$
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what is the slope of this line? simplify your answer and write it as a …
$\frac{1}{3}$
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what is the slope of this line? simplify your answer and write it as a …
3
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what is the slope of this line? simplify your answer and write it as a …
1
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4 find the slope m of the line in the graph below. m = 4
\(4\)
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which of the relationships below represents a function with the same sl…
A. | $x$ | $y$ | |-----|-----| | $-6$ | $12$ | | $-4$ | $9$ | | $-2$ | $6$ | | $0$ | $3$ |
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10. y = -4 slope (m) = y-intercept (b) = 11. y + x = 3 slope (m) = y-in…
slope (\( m \)) = \( 0 \) y - intercept (\( b \)) = \( -4 \) ### Problem 11: \( y + x=3 \) (rewrite as \( y=-x + 3 \))
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solve for x and y by graphing the system of linear equations. drag the …
$(x,y)=(-5,4)$
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6. which points are on the graph of the function rule $f(x) = 10 - 4x$?…
\((-2, 18), (0, 10), (2, 2)\) (la cuarta opción)
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f(x) = x⁴ + 4x² + 3; g(x) = 3x⁴ + 12x³ + 18x² + 12x + 3
For \( f(x) \), factored form is \( \boldsymbol{(x^2 + 1)(x^2 + 3)} \); for \( g(x) \), factored form is \( \boldsymbol{3(x + 1)^4} \). If analyzing the graph, \( f(x) \) is symme…
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3 use numbers from the box to complete the equation a. $0.8 \\times 0.8…
\(0.64\) (if box has 0.64, else 0.6 as a typo) ### Part b
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the graph of $y = \\sqrt{x}$ is the solid black graph below. which func…
$y = \sqrt{x - 4} - 4$
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find the slope of the line that passes through (10, 9) and (4, 2). simp…
$\frac{7}{6}$
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given the function $f(x) = x^2 + 7x + 6$, determine the average rate of…
\( 2 \)
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the function $y = f(x)$ is graphed below. what is the average rate of c…
\(0\)
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solve this system of equations by graphing. first graph the equations, …
The solution to the system of equations is \((-3, -4)\)
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determine all intervals on which the graph of f is decreasing. graph of…
The intervals on which \( f \) is decreasing are \( (-4, - 1)\) and \( (3, 8)\) (assuming the graph's key points and slope analysis. If there are other key points, the intervals m…
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evaluate quadratic functions score: 1/5 penalty: none question given $f…
$-90$
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question given ( f(x) = -x^2 - 4x - 12 ), find ( f(-7) ) answer attempt…
$-33$
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evaluate linear functions score: 4/5 penalty: none question given $g(x)…
$-8$
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question given $f(x) = -4x - 5$, find $f(-4)$. answer attempt 1 out of …
11
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given $h(x) = 2x + 4$, find $h(-1)$. answer attempt 1 out of 2 submit a…
2
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determine whether the following graph represents a function. the graph …
The graph does not represent a function because at least one input is mapped to multiple outputs. For example, the input $x=2$ is mapped to the approximate outputs of $y=4$ and $y…
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use the passage to answer the question. like other mined minerals, gold…
Returning to the gold standard would limit the amount of money in circulation to the amount of gold available, and if gold ran out, that could cause problems.
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17. the value of a certain collectible card in dollars from january 202…
$0 < m < 7$ --- ### Question 18
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5. let $f(x) = 4x^2 + 2x + 1$ and let $g(x) = f(x + k)$. complete each …
When $k=2$: left When $k=-3$: right --- ### Problem 6
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the function $f(x) = -x^2 - 2x + 15$ is shown on the graph. what are th…
The domain is all real numbers. The range is \(\{y|y\leqslant16\}\) (the second option: The domain is all real numbers. The range is \(\{y|y\leqslant16\}\))
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what are the domain and range of this function? image of a coordinate g…
domain: $\{-2, -1, 0, 1, 3\}$ range: $\{-5, 2, 4, 5\}$
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what is the vertex of the graph of the function $f(x) = x^2 + 8x - 2$? …
(-4, -18)
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write a quadratic function to model the graph to the right. f(x) = \\sq…
\(4x^{2}+4\)
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the graph of the function $f(x) = -(x + 3)(x - 1)$ is shown below graph…
The domain is all real numbers, and the range is all real numbers less than or equal to 4. (The corresponding option, assuming the options are labeled as above, would be the third…
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what is the equation of the translated function g(x) if f(x) = x²? ○ g(…
\( \boldsymbol{g(x)=(x - 2)^2+5} \) (corresponding to the option: \( \boldsymbol{\text{O } g(x)=(x - 2)^2+5} \))
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x | f(x) -2 | 3 -1 | -2 0 | -3 1 | 0 2 | 7 what is the rate of change f…
5
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what are the domain and range of this function? image of a coordinate g…
domain: $\{-3, -1, 0, 1\}$ range: $\{-5, -1, 0, 4\}$
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given the function $f(x) = -5x^2 - x + 20$, find $f(3)$.\ \\bigcirc\\ -…
\(-28\) (corresponding to the option: -28)
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which of the following describes the growth rate of the exponential fun…
For each \(x\) increase of 1, the \(y\) increases by a common factor of 3 (the second option)
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write the equation of this line in slope - intercept form. write your a…
$y = 3x-5$
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tables of values for two different functions are given below | x | y | …
The right function grows approximately 21 times faster than the left function over the interval \( 4 < x < 5 \).
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what are the x-intercepts of the function $f(x) = -x^2 - x + 2$? ○ $(-2…
\( (-2, 0) \) and \( (1, 0) \) (corresponding to the first option: \( \boldsymbol{(-2, 0)} \) and \( \boldsymbol{(1, 0)} \))
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the function $f(x) = -(x + 5)(x + 1)$ is shown. what is the range of th…
all real numbers less than or equal to 4
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here is a system of equations. \\begin{cases} y = -5 - 3x \\\\ y = -3x …
Infinitely many solutions
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question the graph of ( y = f(x) ) is the solid black graph below. whic…
\( y = f(x - 5)+2 \) (the option with this formula, usually the third one in the list of options provided in the question)
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anya found the slope of the line that passes through the points (-7, 4)…
She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values.
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sketch the graph of the quadratic function and the axis of symmetry. st…
The equation for the axis of symmetry is \( x = -2 \).
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revisiting exponents & their functions quick check the elephant populat…
A. The elephant population in 1990 is 315, and the population increases by 7.5% each year.
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the graph of the the function f(x) is shown at the right. a. make a tab…
For \( x = 6 \), \( f(x - 5)=\boldsymbol{0} \); for \( x = 7 \), \( f(x - 5)=\boldsymbol{2} \); for \( x = 11 \), \( f(x - 5)=\boldsymbol{4} \); for \( x = 13 \), \( f(x - 5)=\bol…
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name: tyler angoketto date: 1-12-26 per: 1a unit 5: polynomial function…
1. a) As $x \to -\infty$, $f(x) \to -\infty$; as $x \to +\infty$, $f(x) \to +\infty$ b) Odd degree c) Positive 2. a) As $x \to -\infty$, $f(x) \to -\infty$; as $x \to +\infty$, $f…
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ponents & radicals revisiting exponents & their functions back to intro…
The exponential function is \( f(x) = 8 \cdot (0.5)^x \) and \( f(5) = 0.25 \).
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use the table to answer the question. this table shows value of f(x) fo…
\( f(x) = \boldsymbol{2500} \cdot \boldsymbol{(1.05)}^x \)
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revisiting exponents & their functions practice complete this assessmen…
\(x = 38\)
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find the zeros of the function. state the multiplicity of multiple zero…
C. The numbers $-1, 0, 1$ are zeros of multiplicity 1.
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10. when using a table to graph a function, what is the vertical line t…
A. Whether each x - value has exactly one y - value
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graph the equation. then describe the transformation from the parent fu…
A
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a train leaves the station at time t = 0. traveling at a constant speed…
$d = 120t$
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make a table of values for the following equation. then graph the equat…
### Part 1: Table of Values for \( y = |x + 5| \) To create a table of values, we choose several values for \( x \) and calculate the corresponding \( y \)-values using the absolu…
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question 5 while responding to a collision with injuries, an officer ma…
C. Due regard for the public
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make a table of values for the following equation. then graph the equat…
For \( x = -3 \), \( y = 4 \); for \( x = -1 \), \( y = 2 \); for \( x = 0 \), \( y = 1 \); for \( x = 1 \), \( y = 2 \); for \( x = 3 \), \( y = 4 \). The completed table is: | \…