微积分
极限、导数、最优化与函数性质。
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1. rewrite the following expressions as shown in the example: example: …
1. a. $5$ b. $\frac{26}{5}$ or $5\frac{1}{5}$ c. $\frac{27}{4}$ or $6\frac{3}{4}$ 2. a. $12$ b. $16$ c. $44$ d. $42$ e. $15$
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space on the shop floor, bins, carts, or racks are capacity-limiting re…
Delays
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which point of view is able to reveal the thoughts and feelings of all …
3rd person, omniscient
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example: $\frac{2}{3} + \frac{2}{3} + \frac{2}{3} + \frac{2}{3} = \frac…
a. $5$ b. $\frac{26}{5}$ c. $\frac{27}{4}$
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graph the parabola. y = -x² plot five points on the parabola: the verte…
The five points are the vertex \((0,0)\), two points to the left \((-1, -1)\), \((-2, -4)\) and two points to the right \((1, -1)\), \((2, -4)\). To graph the parabola, plot these…
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question 2 10 pts you are standing at the front doors on the first day …
Second person
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which is the slope of the line that passes through the points (-2, 4) a…
slope \( =-\frac{5}{7} \) (the option with this value)
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evaluate. \\( 3\\cdot(7 - 4)^{3} \\)
\(81\)
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answer attempt 2 out of 3 the function is increasing on the interval -9…
The function is increasing on the interval $-9 < x < -4$ (segment 1), decreasing on the interval $-4 < x < 1$ (segment 2), and increasing on the interval $1 < x < 5$ (segment 3).
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1.3 solving piecewise functions cw due: february 4 at 8:00 am grade: 25…
The function is **increasing** on the interval \(-7 < x < -2\) (segment 1), **decreasing** on the interval \(-2 < x < 3\) (segment 2), and **increasing** on the interval \(3 < x <…
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which is the slope of the line that passes through the points (3, 5) an…
slope \( = \frac{2}{5} \) (the option with slope \( = \frac{2}{5} \))
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which of the following is the graph of this quadratic function? y = -3x…
The second graph (the one with x - intercepts around \( x=-2 \) and \( x = 0 \), vertex at \( x=-1 \), y - intercept at \( y = 2 \) and opening downward)
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which of the following is the graph of this quadratic function? $y = \\…
The first graph (the one with vertex at (4, - 3) and y - intercept at (0,1))
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which of the following is the graph of this quadratic function? y = 3x²…
The middle graph (the second graph among the three given graphs) is the graph of the quadratic function \(y = 3x^2+6x - 2\)
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day 1 - please show all of your work! you might need to do it on anothe…
### Computation: 1. $456.9 - 58.3 = 398.6$ 2. $78 \times 125 = 9750$ 3. $67.8 \times 2.5 = 169.5$ ### Fractions / Decimals: 1. $\frac{1}{8}, 0.135, \frac{1}{3}, 0.42, \frac{3}{4}$…
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composition of functions and modeling analyzing composition of function…
The correct statements are: 1. For $f(x)=4x$, $g(x)=x^2$: so function composition is not commutative 2. For $f(x)=2x-5$, $g(x)=0.5x-2.5$: so function composition is commutative 3.…
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5. $x - y = 5$ $-3x + y = -1$
The solution to the system of equations is \(x=-2,y = - 7\)
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Question was provided via image upload.
Vertex: $(-4, 3)$ Equation of axis of symmetry: $x=-4$ *(For graphing: Plot the vertex $(-4,3)$, since $a=-2<0$ the parabola opens downward. Use the axis of symmetry $x=-4$ (dashe…
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divide. give the exact answer, written as a decimal. \\(\\begin{array}{…
4225.5
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graph the equation $y = -x^2 + 2x + 3$ on the accompanying set of axes.…
The vertex of the parabola is \((1, 4)\)
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look at this graph: what is the y-intercept?
$0$
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the movement of the progress bar may be uneven because questions can be…
17
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find the equation of the line written in point - slope form with the gi…
\(y + 2=3(x - 7)\)
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the graph shows g(x), which is a translation of $f(x)=x^2$. write the f…
$g(x)=x^2 - 1$
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determine the domain on which the following function is increasing
$x > 2$ or in interval notation: $(2, \infty)$
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¿cuál es el valor de? $\\log_{625} 5$?\ $\\frac{1}{4}$\ $4$\ $-\\frac{1…
$\frac{1}{4}$
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what is the slope of this line? simplify your answer and write it as a …
\(-3\)
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write the equation of the line in fully simplified slope - intercept fo…
$y = -\frac{1}{2}x - 8$
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function a and function b are linear functions. function a (graph of a …
The y-value of Function A when x = 1 is greater than the y-value of Function B when x = 1.
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graph this line using the slope and y-intercept: $y = -\frac{7}{6}x + 2…
The line passes through points $(0, 2)$ and $(6, -5)$, with a slope of $-\frac{7}{6}$ and y-intercept at $(0,2)$.
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subtract. write your answer as a fraction in simplest form.\\(\frac{9}{…
$\frac{3}{5}$
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given the functions $f(x) = x^4$ and $g(x) = 6 cdot 2^x$, which of the …
$f(9) > g(9)$
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graph the equation shown below by transforming the given graph of the p…
The graph of $y=|3x|$ is a horizontally compressed (by factor $\frac{1}{3}$) version of $y=|x|$, with vertex at $(0,0)$, passing through points like $(1,3)$, $(-1,3)$, $(2,6)$, $(…
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look at this graph: what is the minimum value of this function?
0
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graph this line: $y + 4 = \\frac{7}{2}(x + 2)$ click to select points o…
Plot the points $(-2, -4)$ and $(0, 3)$, then draw a straight line through them to graph the line.
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the graph of a function ( h ) is shown below. use the graph of the func…
2
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fill in the blanks below. (a) find the slope of the line passing throug…
(a) Slope: $0$ (b) Slope: Undefined
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solve the system of equations by graphing. first graph the equations, a…
The solutions are \((0, -6)\) and \((6, 0)\).
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which of these forms of business is a hybrid form of business? a limite…
D. Limited Liability Companies
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2 write an equation for each linear function described. a. the function…
s: a. $y=\frac{3}{2}x+\frac{9}{2}$ (or $y = 1.5x + 4.5$) b. $y=\frac{4}{5}x + 2$ (or $y=0.8x + 2$)
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the height of a ball (in feet) after t seconds is given by the quadrati…
a. 3 seconds b. 115 feet
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7 × 10 + 3 × 30
160
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find two functions f and g such that (f ∘ g)(x) = h(x). (there are many…
\( f(x)=\frac{2}{x^2} \), \( g(x)=4x + 5 \) (Note: There are other possible answers, for example, \( g(x)=4x \), \( f(x)=\frac{2}{(x + 5)^2} \) is also a valid pair of functions a…
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which business form(s) does not benefit from pass-through taxation? a l…
C. Corporations
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55 - (5² × 3) - 5²
$5$
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in exercises 1 - 6, determine whether the equation represents an expone…
81
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which of these is not one of the basic business forms? a limited liabil…
B. Limited Partnership
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5 × (92 - 18)
# Explicación: ## Paso 1: Resolver la resta del paréntesis $92 - 18 = 74$ ## Paso 2: Multiplicar el resultado por 5 $5 \times 74 = 370$ # Respuesta: 370
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3. 12 + (4²) - 11 =
17
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find $8 \\times 0.3$. $\\begin{align*}8 \\times 0.3 &= 8 \\times (3 \\t…
right
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use transformations of the graph of $f(x)=x^2$ to determine the graph o…
B. The graph of $f(x)=x^2$ should be shifted 3 units to the left.
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use transformations of the graph of $f(x)=x^{2}$ to determine the graph…
B. The graph of $f(x)=x^2$ should be shifted 3 units to the left.
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what is a benefit associated with free trade? increased government reve…
B. enhanced innovation and technology
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find ( 5 \times 0.9 ). find the product of the whole numbers. ( 5 \time…
First, the number in the box is 45. And the final result of \(5\times0.9\) is \(4.5\).
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use transformations of f(x)=x² to graph the following function. g(x)=x²…
C. The graph of $f(x)=x^2$ should be shifted 5 units up.
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find $5 \\times 0.9$. first, represent the decimal using place value an…
4.5
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globalization is the process of limiting exchange of goods and services…
connecting the world over time.
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globalization is the process of limiting exhange of goods and services.…
connecting the world over time.
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graphing a slope drag the purple point to graph a slope of $m = \\frac{…
To graph the slope \( m = \frac{3}{4} \), from the initial purple point, move 4 units to the right (horizontal direction, positive x - direction) and 3 units up (vertical directio…
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x = 0 to x = 2; increasing; x = 2 to x = 4; x = 3 to x = 5; x = 4 to x …
- **Increasing**: \( x = 0 \) to \( x = 2 \), \( x = 2 \) to \( x = 4 \), \( x = 0 \) to \( x = 4 \), \( x = 3 \) to \( x = 5 \) - **Decreasing**: \( x = 4 \) to \( x = 7 \), \( x…
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use transformations of $f(x)=x^2$ to graph the following function. \\( …
A. The graph of $f(x)=x^{2}$ should be shifted 5 units down.
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use transformations of $f(x)=x^{2}$ to graph the following function.\ \…
A. The graph of $f(x)=x^2$ should be shifted 5 units down.
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review questions: outlining directions: read the lesson and complete th…
## I. The Election of 1912 A. Progressive (Bull Moose); William Howard Taft; Woodrow Wilson B. New Nationalism C. New Freedom D. Woodrow Wilson ## II. Wilson’s Reforms A. Underwoo…
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next, find the product. 9 × 0.02 = 9 × 2 hundredths = hundredths
18
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here are graphs of two exponential functions, f and g. if ( f(x) = 100 …
A. $\frac{1}{3}$
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find two functions f and g such that (f ∘ g)(x) = h(x). (there are many…
\( f(x)=x^3 \), \( g(x)=6 - x \) (Note: There are other possible answers, for example, \( f(x)=(x)^3 \) and \( g(x) = 6 - x \) is a valid pair of functions for the composition.)
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now, write the product as a decimal. 6 × 0.6 = 6 × 6 tenths = 36 tenths…
$3.6$
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use transformations of $f(x)=x^2$ to graph the following function.\\ $g…
D. The graph of $f(x)=x^2$ should be shifted 4 units up.
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find two functions f and g such that (f ∘ g)(x) = h(x). (there are many…
\( f(x)=x^3 \), \( g(x)=6 - x \) (Note: There are other valid pairs of functions as well, but this is one common solution.)
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use the graph of ( y = f(x) ) to graph the function ( g ).( g(x) = f(2x…
The graph of $g(x)=f(2x)$ is a horizontal compression of $y=f(x)$ by a factor of $\frac{1}{2}$, with key points $(-3, 0)$, $(-1, -7)$, $(0, 0)$, $(3, 0)$, $(4, 7)$ connected seque…
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find two functions f and g such that (f ∘ g)(x) = h(x). (there are many…
\( f(x)=x^2 \), \( g(x)=4x + 6 \) (So the pair is \( (x^2, 4x + 6) \))
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analyzing tables a local maximum of the function ( f(x) ) occurs for wh…
-1
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question 7 for the following exercise, determine the interval(s) on whi…
Increasing: $(-1, \infty)$ Decreasing: $(-\infty, -1)$
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find $f \\circ g$ and $g \\circ f$. \\( f(x) = \\dfrac{7}{x^2 - 1},\\ g…
\( \frac{x^2 + 6}{x^2 - 1} \) (or \( \frac{7}{x^2 - 1} + 1 \)) #### Domain of \( f \)
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for the following exercise, determine the interval(s) on which the func…
Increasing: $(-9, \infty)$ Decreasing: $(-\infty, -9)$
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for the following exercise, use a graphing utility to estimate the loca…
Furthest left local extrema: $(0, 0)$ Furthest right local extrema: $(8, 4)$ Increasing on the interval: $(0, 8)$ Decreasing on the interval: $(-\infty, 0) \cup (8, \infty)$
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12 $\\frac{5}{6} \\cdot 9 =$
$\frac{15}{2}$ (or $7\frac{1}{2}$)
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9 2/3 · 7 =
$\frac{14}{3}$ (or $4\frac{2}{3}$)
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for the following exercise, use a graphing utility to estimate the loca…
Local extrema: (local minimum at $x=9$, $f(9)=-2185$) Increasing on the interval: $(9, \infty)$ Decreasing on the interval: $(-\infty, 9)$
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actions. 8 (\boldsymbol{\frac{3}{4} cdot 9 =}) ______
$\frac{27}{4}$ or $6\frac{3}{4}$
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① $y = -x - 3$ $y = x - 1$ answer: ② $2x + 2y = -6$ $y = -x - 3$ answer…
\( x = -1, y = -2 \) ### Problem 2: Solve the system \( \begin{cases} 2x + 2y = -6 \\ y = -x - 3 \end{cases} \)
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graph this line using the slope and y-intercept: $y = -\frac{1}{2}x$ cl…
The line passes through points such as $(0,0)$, $(2, -1)$, and $(-2, 1)$, forming a straight line with slope $-\frac{1}{2}$ and y-intercept at the origin.
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graph this line: \\( y - 2 = -\frac{10}{3}x \\) click to select points …
Plot the points $(0, 2)$, $(3, -8)$, and $(-3, 12)$, then draw a straight line through them to graph the line.
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graph this line: $y + 3 = -\frac{6}{5}(x + 3)$ click to select points o…
Plot the points $(-3, -3)$, $(2, -9)$, and $(0, -6.6)$, then draw a straight line through them to graph the line.
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1. according to the text, why did louis xiv make nobles live at versail…
1. B. He wanted to keep them busy so they couldn't rebel [fight back]. 2. Louis XIV had total control; William & Mary had limits. Louis XIV ignored the people's wishes; William & …
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graph this line: $y + 7 = \\frac{1}{5}(x - 2)$ click to select points o…
Plot the points $(2, -7)$ and $(7, -6)$ (or $(0, -7.4)$), then draw a straight line passing through them to graph the line.
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today, almost every career path is open to men, but women are still lim…
F
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graph this line: $y - 3 = -\frac{1}{2}(x - 6)$ click to select points o…
Plot the points $(6, 3)$, $(0, 6)$, and $(2, 5)$, then draw a straight line through them to graph the line.
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graph this line: $y + 2 = -\frac{1}{3}x$ click to select points on the …
Plot the points $(0, -2)$, $(3, -3)$, and $(-3, -1)$, then draw a straight line through them.
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graph this line using the slope and y-intercept: y = -2x - 1 click to s…
1. Plot the y-intercept point: $(0, -1)$ 2. Plot a second point using the slope: $(1, -3)$ (or $(-1, 1)$) 3. Draw a straight line connecting the points, extending it across the gr…
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evaluate the function $f(x)=x^2 + 3x + 1$ at the given values of the in…
a. $f(-3)=1$ b. $f(x+1)=x^2+5x+5$ c. $f(-x)=x^2-3x+1$
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graph this line using intercepts; x + 2y = 6 click to select points on …
The line passes through the x-intercept $(6, 0)$ and y-intercept $(0, 3)$; connecting these two points gives the graph of $x + 2y = 6$.
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4. constitutional monarchy * 1 point a. a system where the king has tot…
B. A system where the King's power is limited by laws and shared with a legislature
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if $f(x)=\frac{x}{2}+8$, what is $f(x)$ when $x = 10$? ○ 4 ○ 9 ○ 13 ○ 36
13 (Option C: 13)
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graph this line using the slope and y-intercept: $y = -\frac{7}{3}x + 6…
1. Plot the y-intercept point $(0, 6)$ on the graph. 2. Plot the second point $(3, -1)$ on the graph. 3. Plot the third point $(6, -8)$ on the graph. 4. Draw a straight line conne…
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use the aleks graphing calculator to solve the system of equations. y=2…
\((0.71, 2.42)\)
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the functions f(x) and g(x) are graphed. at which points do the two gra…
$f(0) = g(0)$ and $f(2) = g(2)$
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if $f(x) = 5x + 40$, what is $f(x)$ when $x = -5$? -9 -8 7 15
15
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graph this line using the slope and y-intercept: $y = \\frac{9}{7}x - 7…
The line passes through points $(0, -7)$ and $(7, 2)$, with a straight line connecting these points extending across the coordinate grid.
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the graph contains two lines, ( g(x) ) (red) and ( f(x) ) (blue), on a …
$\boldsymbol{f(-2) = g(-2)}$