Calculus
Limits, derivatives, optimization, and behavior of functions.
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read the excerpt from amy tans essay \mother tongue.\ i know this for a…
"when I was growing up"
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if f is an odd function, why is \\(\\int_{-a}^{a} f(x) \\, dx = 0\\)? c…
B. Since f is odd, f is symmetric about the origin. Therefore, $\int_{-a}^{0} f(x) dx = -\int_{0}^{a} f(x) dx ightarrow \int_{-a}^{0} f(x) dx + \int_{0}^{a} f(x) dx = 0 ightarrow …
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for items 1–2, identify the following information for the function of e…
\(-\frac{25}{4}\) (or \(-6.25\))
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28. -5.2 + 6.089 type a response
0.889
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29. 0.15×(-0.6)
$-0.09$
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32. -50.8 ÷ 5
$-10.16$
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5 + 2³ × 4
37
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7) the system of inequalities below represents the constraints associat…
D (the graph with the circle, representing the region that satisfies \(x\geq0\), \(y\geq0\), \(y\leq3x\), and \(5x + 3y\leq18\))
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5. graph the system of equations, and then estimate the solution. $y = …
The solution (intersection point) is $(-2.5, -1)$ To graph: 1. For $y=2x+4$: plot y-intercept $(0,4)$, use slope 2 to plot $(1,6)$ and $(-1,2)$, draw line. 2. For $y=-x-3.5$: plot…
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graphs, functions, and sequences comparing properties of linear functio…
### Part (a) To determine which functions have \( y \)-intercepts greater than \(-4\), we find the \( y \)-intercept for each function: - **Function 1**: The \( y \)-intercept is …
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exercises simplify the quotient. 44. \\(\\frac{\\sqrt{5}}{\\sqrt{10}}\\)
$\frac{\sqrt{2}}{2}$
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12 ÷ (2 + 4) × 3
6
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myra is training for a triathlon and needs to swim a certain distance f…
The total distance of Myra's workout is 500 yards.
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read the excerpt from herbert hoovers ugged individualism\ speech, deli…
To solve this, we analyze the excerpt for reasons Hoover supported limited federal response: 1. Analyze the first highlighted - like part: "It would impair the very basis of liber…
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the equation $y = -2x + 8$ represents the amount $y$ (in fluid ounces) …
If graphing, plot points like \( (0,8) \) and \( (4,0) \) and draw a line. If finding when detergent is used up, \( x = 4 \) days.
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6. a) find the equation of the polynomial that passes through the point…
a) The polynomial equation is $\boldsymbol{y=2x^3 -5x -7}$ b) [Plot instructions: Plot the points (1,-10), (2,-1), (3,32), (4,101), (5,218), (6,395) on a coordinate plane, with x-…
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a. $7\\frac{3}{8} + 3\\frac{1}{4} = $
\(10\frac{5}{8}\)
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identify the equation for this graph. options: y = |x + 2| + 1 y = |x +…
\(y = |x + 2|+1\)
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x | f(x) -2 | 1/8 -1 | 1/4 0 | 1/2 1 | 1 2 | 2 what is the initial valu…
C. \(\frac{1}{2}\) (assuming the options are labeled as A. \(\frac{1}{8}\), B. \(\frac{1}{4}\), C. \(\frac{1}{2}\), D. \(1\))
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what is the initial value of the exponential function shown on the grap…
D. 4 (assuming the options are labeled as A. 0, B. 1, C. 2, D. 4) Wait, the original options are: 0, 1, 2, 4. So the correct option is the one with 4. So the answer is 4 (the opti…
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multiplying 2 digits by 2 digits (renaming) 1. ( \begin{array}{r} 22 \\…
1. a. 418, b. 1312, c. 1296, d. 675, e. 960, f. 1694 2. a. 1512, b. 2496, c. 700, d. 2310, e. 957, f. 6300 3. a. 1311, b. 324, c. 2079, d. 1105, e. 1936, f. 1800 4. a. 851, b. 345…
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which function represents g(x), a reflection of f(x) = \\frac{1}{2}(3)^…
\(g(x)=\frac{1}{2}(3)^{-x}\) (corresponding to the option \(g(x)=\frac{1}{2}(3)^{-x}\))
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3. for the first two problems, circle the vertical calculation where di…
The sum of \(3.25\) and \(1\) is \(4.25\).
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the function $f(x)$ is defined as $f(x) = \\frac{1}{3}(6)^x$. which tab…
The first table (the one with \( f(0)=\frac{1}{3} \) and \( g(0)=\frac{1}{3} \), \( f(1)=2 \), \( g(1)=\frac{1}{18} \), etc.)
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lesson 18 multiplying 2 digits by 2 digits multiply 9 ones by 7 put 6 t…
1. a. 726 b. 495 c. 800 d. 713 e. 156 f. 930 2. a. 861 b. 640 c. 400 d. 651 e. 900 f. 140 3. a. 968 b. 280 c. 480 d. 900 e. 169 f. 330 4. a. 770 b. 132 c. 810 d. 288 e. 880
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which is the graph of $f(x) = \\frac{1}{4}(4)^x$? images of four graphs…
The graph with the point \((2, 4)\) (the bottom - most graph) is the graph of \( f(x)=\frac{1}{4}(4)^x \).
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subtract: 3.6 - 7.2 =
$-3.6$
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given ( f(x) = 0.4x ) is transformed to ( g(x) = 0.4(x + 8) ), what tra…
Horizontal shift of \( B \) units to the left (assuming the option with horizontal shift left is the correct one, based on the function transformation rules)
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add. 6.75 + -2.75 =
$4$
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question 5 (multiple choice worth 2 points) (transformations of linear …
\(-9\)
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add. 2.3 + 7.1 =
9.4
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which graph is the sequence defined by the function $f(x) = 3(2)^{x - 1…
The graph with points \((1, 3)\), \((2, 6)\), \((3, 12)\), \((4, 24)\) (or the graph corresponding to the function \( f(x) = 3(2)^{x-1} \) with these points). However, based on th…
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question 4 (multiple choice worth 2 points) (transformations of linear …
The y - intercept of \(g(x)\) is \(9\), so the correct option (assuming the options are presented as, for example, A. 5, B. - 3, C. 9) is C. 9.
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solve the equation by graphing the related function. $x^2 + 2x + 3 = 0$…
A. <The graph with vertex at (-1, 2) opening upward>
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4.6 + -2.4 =
$2.2$
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determine the transformation on $g(t) = 3t + 1$ that results in the fun…
B. Vertical dilation by a factor of 6
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b. calculate the sum vertically. 0.137 + 0.284 ------- .
\(0.421\) (The boxed answer would be \(\boxed{0.421}\) if we follow the LaTeX boxed format for the final answer, but as per the initial instruction, we can present it as is here.)
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what are the domain, range, and asymptote of $h(x) = 6^x - 4$? \\(\\cir…
B. domain: \(\{x \mid x \text{ is a real number}\}\); range: \(\{y \mid y > -4\}\); asymptote: \(y = -4\)
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5. the number of people, p, at a playground after t min is given by $p …
41
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add. 9.75 + -4.75 =
$5$
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add. -2.6 + -5.6 =
$-8.2$
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in some ways it is the work of the american painters and sculptors whic…
They convey a tone of ridicule by mocking the rigidity of conventions for their tendency to limit creativity and turn away new artists.
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passage 1 what is competition from the point of view of the workman? it…
The labor of underpaid workers is used to build up the wealth of the business owners.
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passage 1 passage 2 in the organization of work (1839) french socialist…
Private property limits poor people's access to essential natural resources, and competition lowers their wages.
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question 1 of 10 what restrictions are there on the range of the functi…
C. $H(w) > 0$
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write as a power function: y varies directly with x and y is 12 when x …
\( y = 2x \) (So the first box is \( y \) and the second box is \( 2 \))
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passage 1 passage 2 what is competition from the point of view of the w…
D. By saying the opposite of what he means, Blanc highlights the evils of the current system.
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what equation represents the inverse of $y = (x + 3)^2 + 4$? a. $y = \\…
B. \( y=\pm\sqrt{x - 4}-3 \)
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question 10 (multiple choice worth 2 points) (exploring exponential fun…
The percent rate of change shows 70% growth.
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question 9 (multiple choice worth 2 points) (exploring exponential func…
B. Growth, because the base value is greater than 1 (assuming the second option is labeled B, if original labels were different, adjust the label but the text is "Growth, because …
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what is the base of the function $y = 7(1.35)^x$? is the function class…
B. The base is 1.35, and the function is classified as exponential growth
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question 7 (multiple choice worth 2 points) (exploring exponential func…
60% (the option corresponding to 60%)
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(exploring exponential functions lc) what is the percent rate of change…
26% (corresponding to the option "26%")
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given the exponential function $b(t) = 5(0.22)^t$, is the function clas…
The function is classified as exponential decay because the base is 0.22.
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determine the base of the function $y = -7(19)^x$, and state if the fun…
A. The base is 19, and the function is classified as exponential growth.
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lesson 1.3 multi-digit multiplication multiply 3,263 by 3. multiply 3,2…
1. $15760$ 2. $6012$ 3. $45036$ 4. $65268$ 5. $276246$ 6. $116688$ 7. $1435228$ 8. $373906$ 9. $740430$
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the table of values represents a continuous unrestricted exponential fu…
It represents exponential growth because as \( x \) increases, \( y \) is not approaching 0.
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what is the difference in simplest form? $5\\frac{5}{8} - 3\\frac{1}{4}…
C. $2\frac{1}{2}$ (assuming a typo in the problem's fraction $\frac{1}{3}$ should be $\frac{1}{8}$)
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a total of 6 identical erasers cost $9.60. what was the price for each …
$\$1.60$
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decimals converting a proper fraction with write $\frac{1}{4}$ as a dec…
0.25
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question 1 (2 points) express k(x) in terms of j(x). graph of j(x) and …
$-j(x)$
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a line has a slope of $-2$ and passes through the point $(3,5)$. which …
a. \( y = -2x + 11 \)
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question 1 (2 points) express k(x) in terms of j(x). graph of j(x) and …
Question 1: $k(x) = -j(x)$ Question 2: - Description: Reflection over the x-axis - $g(x) = -f(x)$ Question 3: (No options provided, cannot answer. Please share the options for Que…
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if the slope of a line is -2 and it passes through the point (0, 4), wh…
b. $y = -2x + 4$
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who held the most power in the mayan political structure? (1 point) the…
B. the kings ### Second Question: What impact did trade networks have on Mayan city - states?
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question determine whether the quadratic function shown below has a min…
Maximum value is -1
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determine whether the quadratic function shown below has a minimum or m…
Minimum value, -3
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4. find the equation of the linear function ( r(x) ) that is parallel t…
$r(x)=-\frac{4}{5}x+\frac{16}{3}$
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in his inaugural address, george washington made promises to the countr…
c. He would make sure all government decisions would be based on doing what is right. ### Question 8
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the table below represents a linear function. | $x$ | $y$ | | --- | ---…
B
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the graph shows a quadratic function f(x) and a line ℓ that intersects …
$-\frac{1}{2}$
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what is the slope of this line? the coordinate grid with a blue line pa…
$\boldsymbol{\frac{5}{3}}$ (matches option: $\frac{5}{3}$)
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the graph shows a straight line. based on the diagram, what is the slop…
2
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the u.s. ultimately paid spain 20 million dollars for possession of the…
C. To a moderate extent—The treaty established the dominance of the United States in the Americas.
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graph this line: y - 3 = -4(x - 7) click to select points on the graph.…
To graph the line $y - 3 = -4(x - 7)$: 1. Plot the point $(7, 3)$ (from the point-slope form). 2. Use the slope $-4$: from $(7,3)$, move 1 unit right and 4 units down to plot $(8,…
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9.5 integrating vector - valued functions calculus for problems 1 - 6, …
\(f(t)=\langle2e^{t},e^{3t}+3 angle\) ### Problem 2
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round 5.158 to the nearest hundredth.
5.16
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line k passes through the points (-2, 5) and (4, -4) on the coordinate …
$\frac{-3}{2}$
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line k passes through the points (-2, 5) and (4, -4) on the coordinate …
$-\frac{3}{2}$
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what happens to the value of the expression \\(\\frac{5}{x} + 5\\) as \…
A. It increases.
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describe in words how you would evaluate the function for f(-5). then s…
To evaluate \( f(-5) \) for \( f(x) = 4x - 1 \), substitute \( x=-5 \) into the function, calculate \( 4\times(-5) \) to get -20, then subtract 1 from -20. The value of \( f(-5) \…
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11. how many feet from the rail road crossing may a motorist park their…
11. 50 feet 12. 55mph - 65mph
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what is the slope of the line that passes through (2, -3) and (-2, 10)?…
$-\frac{13}{4}$
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1.6: homework - polynomial and rational functions score 20/80 answered:…
The real solutions are \(x\approx - 1.83\), \(x = 2\), \(x\approx3.83\) (accurate to two decimal places)
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name:______ date:______ period:____ order of operations color by number…
\(56\) ### Problem 2: \(8 + 5^2 - 4\)
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which expression has a product of 540? a. 9×40 b. 5×60 c. 5×40 d. 9×60
D. \(9 \times 60\)
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how was the magna carta important to the development of the u.s. legal …
a. It promoted the idea of social contract, especially protection for individual rights. d. It declares that the Constitution and federal laws are the highest laws in the nation. …
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how was the magna carta important to the development of the u.s. legal …
a. It promoted the idea of social contract, especially protection for individual rights. ### Question 2
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graph the solution to this system of inequalities in the coordinate pla…
Para graficar la solución: 1. Dibuja la línea **discontinua** \( y = \frac{2}{3}x + 4 \) (por la desigualdad \( 3y > 2x + 12 \)). 2. Dibuja la línea **continua** \( y = -2x - 5 \)…
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1. renting would be most appropriate for people who ______. a) want to …
C) have limited funds currently available
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** this is a 2 - page document! ** verifying inverses directions: deter…
The function \(f(x)=\frac{3}{4}x + 3\) has an inverse. The inverse function is \(f^{-1}(x)=\frac{4}{3}x - 4\) and the domain of \(f(x)\) (and the range of \(f^{-1}(x)\)) is \((-\i…
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complete the text with the best transition. farmers markets are often p…
However, research suggests that
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volume of a cylinder score:4/5 penalty: 0.25 off question what is the v…
56.5
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9 multiple choice 1 point the system of linear equations $5x + 3y = 3$ …
b) (3, -4)
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90. production cost a small - appliance manufacturer finds that if he p…
s: (a) The graph is a straight line passing through \((0, 3000)\) and \((500, 6000)\) (or other suitable points) with \(x\) as the number of toaster ovens and \(y\) as cost. (Grap…
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b. \\(\\log 2 + \\log x = \\log 38\\)
$x = 19$
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20 \\( \\overrightarrow{pq} = \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} …
$\begin{pmatrix} 7 \\ 3 \end{pmatrix}$
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14. divide. express the quotient as a decimal. round to the nearest tho…
0.517
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2. (a) complete the table for $y = x^2 - 2x - 4$ | $x$ | $-2$ | $-1$ | …
The completed table is: | \( x \) | -2 | -1 | 0 | 1 | 2 | 3 | 4 | | --- | --- | --- | --- | --- | --- | --- | --- | | \( y \) | 4 | -1 | -4 | -5 | -4 | -1 | 4 | ### Part (b) To dr…
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1. (a) complete the table of values for $y = x^2 + x$.\ \ | $x$ | $-3$ …
The completed table is: | \( x \) | \( -3 \) | \( -2 \) | \( -1 \) | \( 0 \) | \( 1 \) | \( 2 \) | \( 3 \) | |---------|---------|---------|---------|--------|--------|--------|--…