微積分
極限、導數、最優化與函數性質。
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create a table of values to show that the exponential expression 3(2)^x…
The table of values is: | \( x \) | \( 3x^2 + 2x \) | \( 3(2)^x \) | |--------|----------------|-------------| | 0 | 0 | 3 | | 1 | 5 | 6 | | 2 | 16 | 12 | | 3 | 33 | 24 | | 4 | 56…
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2. an equation is shown. ( y = 3|x + 2| - 6 ) use the coordinate grid t…
The graph of \( y = 3|x + 2| - 6 \) is a V - shaped graph with vertex at \((-2, -6)\), right branch passing through points like \((-1, -3)\), \((0, 0)\) etc. (with slope \( 3 \)) …
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divide. write the quotient in simplified form. $-\frac{11}{12} \\div 22…
\(-\frac{1}{24}\) (and the correct choice is A)
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which of the functions shown is the graph of $y = -(x + 1)^3$?
\( A(x) \) (the graph labeled \( A(x) \))
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which of the functions shown is the graph of y = x³ + 3?
The function \( A(x) \) (the pink - colored graph) is the graph of \( y = x^3+3 \).
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multiply. write the product in simplest form $-\frac{4}{7} cdot \frac{2…
\( -\frac{8}{77} \)
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the functions s and t are defined as follows. s(x)=2x+2 t(x)=-2x² -2 fi…
$-38$
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unit 7 review: cube & cube root which of the functions shown is the gra…
\( C(x) \)
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if you stretch your own canvases, you can get stretcher bars in just ab…
8. 16 9. First, you use your ruler to make a small mark at every inch at the top of the paper. Next, you place the ruler at the bottom and make a small mark at every inch. Followi…
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$-\frac{3}{11}+\frac{5}{7}=square$
\(\frac{34}{77}\)
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add. \\frac{2}{3}+\\left(-\\frac{5}{9}\ ight)
$\frac{1}{9}$
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which of the following radical functions has a domain of $x \\geq -2$ a…
C. \(h(x)=-\sqrt{x + 2}+3\)
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select the radical function with a domain of $x\\geq -2$. a. $a(x) = 3\…
C. \(C(x)=\sqrt[4]{x + 2}+10\)
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select all the radical functions with a range that includes all real nu…
A. \(A(x)=2\sqrt[3]{x + 4}\), D. \(D(x)=\sqrt[7]{2x}-8\)
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221÷13 =? \\square ÷13 = \\square
$221 \div 13 = 17$ $\boldsymbol{221} \div 13 = \boldsymbol{17}$
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5. find the inverse of $f(x) = -\frac{2x + 1}{3}$ rewrite as y = switch…
$f^{-1}(x) = \frac{-3x -1}{2}$
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a student says: we cannot subtract 1.97 from 20 because 20 does not hav…
No
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1. \\(\\begin{array}{r}5 \\\\ \\times 0.35\\end{array}\\) 2. \\(\\begin…
1. $1.75$ 2. $13$ 3. $0.07725$ 4. $102.9054$ 5. $0.00214$ 6. $0.72$ 7. $1.7$ 8. $5.72$
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write 9.6 as a mixed number and as an improper fraction. do not try to …
mixed number: $9\frac{6}{10}$ improper fraction: $\frac{96}{10}$
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104÷4=? type a helper equation to divide the problem into friend blank …
Helper equation: $100\div4 + 4\div4 = 25 + 1$ Final result: $26$
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write 8.56 as a mixed number and as an improper fraction. do not try to…
mixed number: $8\frac{56}{100}$ improper fraction: $\frac{856}{100}$
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504÷18=? □ ÷18=□
Helper equation: $504 \div 9 \div 2 = 28$ Final result: $28$
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write the equation of the line in fully simplified slope - intercept fo…
\(y=-2x + 4\)
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type a helper equation to divide the problem into frie 247÷13=? \\squar…
Helper equation: $130 \div 13 = 10$ Final answer: $19$
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how does the graph of $y = 3^x$ compare to the graph of $y = 3^{-x}$? t…
The graphs are reflected across the \( y \)-axis.
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identifying domain and range of exponential fun identify the domain and…
The domain of this function is all real numbers (in interval notation, \( (-\infty, \infty) \)). The range of this function is all positive real numbers (in interval notation, \( …
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ying asymptotes of exponential functions identify the horizontal asympt…
\( y = -3 \) (corresponding to the option \( y=-3 \))
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in 4 - 6, evaluate each expression. 4. $5^2 - 9 \\div 3$ 5. $8 + 6 - 2 …
4. 22 5. 1 6. 2
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ying asymptotes of exponential functions identify the horizontal asympt…
\( y = 0 \)
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the function $f(x)$ is graphed below. write the domain and range using …
Domain: \(-\infty < x<\infty\) Range: \(y\leq8\) (or \(-\infty < y\leq8\))
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the function $f(x)$ is graphed below. write the domain and range using …
Domain: \( -\infty < x < \infty \) Range: \( -\infty < y \leq 5 \)
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om 5.1, 5.2, 5.3 score: 7/14 answered: 3/7 question 4 graph the followi…
\((-3, -1)\)
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given the function below, fill in at least 3 rows of the table of value…
| $x$ | $-\frac{2}{3}x$ | $y = -\frac{2}{3}x - 1$ | |-----|------------------|---------------------------| | $-3$ | $2$ | $1$ | | $0$ | $0$ | $-1$ | | $3$ | $-2$ | $-3$ |
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erstanding graphs of exponential functions the graph of $y = b^x$ is sh…
\(\frac{1}{2}\)
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answers must be written as fractions in simplest form, but you only nee…
| $x$ | $\frac{1}{2}x$ | $y=\frac{1}{2}x-5$ | |-----|----------------|---------------------| | $-4$ | $-2$ | $-7$ | | $0$ | $0$ | $-5$ | | $2$ | $1$ | $-4$ |
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identifying domain and range of exponential functions identify the doma…
The domain of this function is all real numbers (or \(\mathbb{R}\) or \((-\infty,\infty)\)). The range of this function is \((3,\infty)\).
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divide. write your answer in sim\\(\\frac{6}{5} \\div \\frac{7}{6}\\)
$\frac{36}{35}$ or $1\frac{1}{35}$
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given the function below, fill in at least 3 rows of the table of value…
| $x$ | $-\frac{5}{4}x$ | $y = -\frac{5}{4}x - 4$ | |-----|-----------------|--------------------------| | $-4$ | $5$ | $1$ | | $0$ | $0$ | $-4$ | | $4$ | $-5$ | $-9$ |
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simplify the expression. select ot a real number\ if applicable. \\sqrt…
$-\frac{3}{4}$
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add: 89 + -1 = save answe
88
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add: -8 + -4 =
-12
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add: -15 + 99 = \\boxed{}
84
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add: 2 + -8 = save answe
-6
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add: -1 + 77 = save answer
76
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complete ordered pairs for the equation, and then graph the equation. 4…
4
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enter the correct answer that completes the sentence below. the y-inter…
\((0,3)\)
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compute the discriminant. then determine the number and type of solutio…
0 Additionally, since the discriminant is 0, the quadratic equation has **one real repeated rational solution**.
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look at this graph: is this relation a function? yes no
yes
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multiply. \\(dfrac{3}{8} \\times 64\\)
24
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a line passes through the point (-2,-3) and is perpendicular to the lin…
y=-2x-7 (Option C)
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question 15 a line passes through the point (0,2) and is perpendicular …
C. $y=4x+2$
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question 13 what is the slope of a horizontal line? -1 0 undefined 1
0 (Option: 0)
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question 12 if the equation of a line is y = 7x - 5, what is its slope?…
B. 7
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question 11 a line has a slope of -3/4. which of the following could be…
Change in y = -3, change in x = 4 Change in y = 3, change in x = -4
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complete the table to investigate dilations of exponential functions. w…
\( y = 3\cdot2^{x} \)
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graph the equation $y = |x| + 5$. let $x = -3, -2, -1, 0, 1, 2,$ and $3…
Completed table: | x | y | |----|----| | -3 | 8 | | -2 | 7 | | -1 | 6 | | 0 | 5 | | 1 | 6 | | 2 | 7 | | 3 | 8 | Correct graph: A.
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multiply. write your answer as a fraction in simplest form.\\(\frac{2}{…
$\frac{4}{7}$
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find seven ordered pairs to the equation ( y = x^2 - 7 ). then determin…
The seven ordered pairs are (-3, 2), (-2, -3), (-1, -6), (0, -7), (1, -6), (2, -3), (3, 2)
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a ball is thrown from an initial height of 2 feet with an initial upwar…
\( t = 0.55 \) or \( t = 1.14 \) seconds
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to make $48 + 34$ easier to solve, lou decides to first add on from 48 …
82
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7.3) _____ legislators, judges, and presidents ____ a. are the three br…
7.3) D. are constantly having to interpret the Constitution 7.4) prohibit; religion; abridge freedom of speech; abridge freedom of the press; assemble; petition the government for…
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identifying the domain and range of an exponential function use the gra…
- The domain of the function is \( -\infty \) to \( \infty \) because an exponent can be any real number. - The range of the function is \( 0 \) to \( \infty \) because \( 4^x \) …
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divide and express the result in standard form. \\(\frac{3}{8 - i}\\) \…
$\frac{24}{65} + \frac{3}{65}i$
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soraya wants to sign up for a gym membership at gym club premium. she n…
20
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amina opens a savings account. she starts her savings account with 20 d…
15
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complete the table to investigate dilations of exponential functions. |…
\(a = 1\), \(b = 3\), \(c = 1\), \(d = 2\), \(e = 6\), \(f = 8\)
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tajiri opens a savings account. each week he adds the same amount of mo…
The slope means that Tajiri adds 15 dollars to his account each week.
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use what you know about translations of functions to analyze the graph …
1. The parent function \( y = 0.5^x \) is \(\boldsymbol{\text{decreasing}}\) across its domain because its base, \( b \), is such that \(\boldsymbol{0 < b < 1}\). 2. The function,…
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tajiri opens a savings account. each week he adds the same amount of mo…
15
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12. without graphing, determine if each polynomial function has line sy…
a) Point symmetry about the origin (odd function) b) Line symmetry about the y-axis (even function) c) Neither symmetry
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now, solve. 9·6 = 9 groups of 6 9·(-6) = 9 groups of -6 -54 54
- $9 \cdot 6$ (9 groups of 6) matches $\boldsymbol{54}$ - $9 \cdot (-6)$ (9 groups of -6) matches $\boldsymbol{-54}$
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12 select the correct answer from each drop - down menu. consider the f…
As the value of x increases, the value of $f(x)$ increases The x-intercept is the point (-3, 0)
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find the amplitude (if one exists), label key points. show at least two…
The period of the function \( y = 2\sin(\pi x + 3)-3 \) is \( 2 \).
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6. does the graph represent a linear or nonlinear function? explain.
The graph represents a nonlinear function. It is a curved line, not a straight line, so it does not have a constant rate of change required for a linear function.
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samara started drumming lessons and learns 4 songs each month. lets bre…
$4$
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samara is knitting a scarf for her mom. she knits 4.5 centimeters of sc…
The missing horizontal distance value is $\boldsymbol{2}$, and the slope of line $m$ is $\boldsymbol{4.5}$
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the graph of ( y = f(x) ) is graphed below. what is the end behavior of…
as \(x \to -\infty, y \to \infty\) and as \(x \to \infty, y \to \infty\)
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the graph of ( y = f(x) ) is graphed below. what is the end behavior of…
as \( x \to -\infty, f(x) \to \infty \) and as \( x \to \infty, f(x) \to \infty \) (the third option in the list of choices)
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answer as ( x \to -infty ), ( f(x) \to infty ) and as ( x \to infty ), …
as \( x \to -\infty, f(x) \to -\infty \) and as \( x \to \infty, f(x) \to \infty \) (the third option in the list of choices)
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the graph of ( y = f(x) ) is graphed below. what is the end behavior of…
as \(x \to \infty, f(x) \to -\infty\) and as \(x \to -\infty, f(x) \to -\infty\) (the option with this description)
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the graph of $y = f(x)$ is graphed below. what is the end behavior of $…
As \( x \to -\infty \), \( y \to -\infty \) and as \( x \to \infty \), \( y \to \infty \) (the last option among the given choices which should be in the form like "as \( x \to -\…
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the graph of $y = f(x)$ is graphed below, what is the end behavior of $…
as \( x \to -\infty, f(x) \to \infty \) and as \( x \to \infty, f(x) \to -\infty \) (the option with this description)
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find seven ordered pairs to the equation $y = 8 - x^2$. then determine …
When \(x=-3\), \(y=-1\) When \(x=-2\), \(y=4\) When \(x=-1\), \(y=7\) When \(x=0\), \(y=8\) When \(x=1\), \(y=7\) When \(x=2\), \(y=4\) When \(x=3\), \(y=-1\)
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graph the equation $y = 5|x|$. let $x = -3, -2, -1, 0, 1, 2,$ and $3$. …
C. (The V-shaped graph opening upwards with vertex at (0,0) passing through (-3,15), (-2,10), (-1,5), (1,5), (2,10), (3,15))
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the graph of ( y = f(x) ) is graphed below. what is the end behavior of…
as \( x \to -\infty \), \( y \to \infty \) and as \( x \to \infty \), \( y \to -\infty \)
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graph the equation $y = -\frac{2}{3}x$. let $x = -9, -6, -3, 0, 3, 6,$ …
A. The line passing through points (-9, 6), (-6, 4), (-3, 2), (0, 0), (3, -2), (6, -4), (9, -6)
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graph the equation $y = -\frac{2}{3}x$. let $x = -9, -6, -3, 0, 3, 6$, …
6 Additionally, here are the y-values for all given x-values for full reference: | x | y | |----|---| | -9 | 6 | | -6 | 4 | | -3 | 2 | | 0 | 0 | | 3 | -2 | | 6 | -4 | | 9 | -6 |
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some people say that allowing internet access in schools is a bad idea …
It provides a solution to the problem suggested by the counterclaim.
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graph the equation ( y = x - 1 ). let ( x = -3, -2, -1, 0, 1, 2 ), and …
-4
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answer as ( x \to infty, y \to infty ) and as ( x \to -infty, y \to -in…
as \(x\to\infty,y\to\infty\) and as \(x\to-\infty,y\to-\infty\) (the first option in the list of options provided)
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graph the equation $y = x + 5$. let $x = -3, -2, -1, 0, 1, 2,$ and $3$.…
4 Additionally, for the complete set of x-values provided: When $x=0$, $y=0+5=5$ When $x=1$, $y=1+5=6$ When $x=2$, $y=2+5=7$ When $x=3$, $y=3+5=8$ The full table of values is: | x…
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graph the equation $y = x + 5$. let $x = -3, -2, -1, 0, 1, 2,$ and $3$.…
3
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graph the equation $y = x + 5$. let $x = -3, -2, -1, 0, 1, 2,$ and $3$.…
2
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the graph of ( y = f(x) ) is graphed below. what is the end behavior of…
as \( x \to -\infty,y \to \infty \) and as \( x \to \infty,y \to \infty \) (the option with this description)
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the graph of $y = f(x)$ is graphed below. what is the end behavior of $…
as \( x \to \infty,y \to \infty \) and as \( x \to -\infty,y \to -\infty \) (the first option in the list of answer choices)
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the cost in dollars to produce x cups of lemonade is represented by the…
34 cups
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start by finding the change in vertical and horizontal distance from (2…
Change in number of toys (horizontal distance): 2 Change in total cost (vertical distance): 10 Slope of the line: 5
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a restaurant charges $12 for a plain medium pizza and $1.50 for every t…
$1.5$
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use the graph of g(x) to complete the table. x | g(x) -9 | -8 | -4 | 2
| $x$ | $g(x)$ | |-----|--------| | -9 | 8 | | -8 | 5 | | -4 | 2 |
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use the graph of ( f(x) ) to complete the table. the table has columns …
For $x=-7$, $f(x)=0$ For $x=5$, $f(x)=-3$ Completed table: | $x$ | $f(x)$ | |-----|--------| | -10 | -2 | | -7 | 0 | | 5 | -3 |