微积分
极限、导数、最优化与函数性质。
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solve each linear system by graphing. write your solution as an ordered…
s: - First system: No solution (parallel lines) - Second system: \( (0, 2) \)
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which of these equations shifts a radical equation right 1 time and up …
\( y = \sqrt{x - 1}+2 \) (the first option, usually presented as the yellow - colored option in the given choices)
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28) ** solve: \\(\\log_{4}(2x) + \\log_{4}(x + 2) = 2\\)
$x = 2$
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14. one large box and two small boxes weigh a total of 50 pounds. two l…
The inequality is \( 3x + y\leq30 \) (or \( 30x + 10y\leq300 \)). To graph it, draw the line \( y=-3x + 30 \) (a straight line with slope - 3, y - intercept 30, and x - intercept …
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find the zeros of $h(x) = -x^3 - 2x^2 + 9x + 18$. $x = -3$ $x = -4$ $x …
Zeros: $x=-3$, $x=-2$, $x=3$ Correct graph: The bottom-left graph with x-intercepts $(-3,0)$, $(-2,0)$, $(3,0)$
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find the zeros of $f(x)=x^3 + x^2 - 6x$. $x=-4$ $x=-1$ $x=2$ $x=-3$ $x=…
Zeros: $x=-3$, $x=0$, $x=2$ Graph: The top-right graph (opening upward on the right, downward on the left, crossing x-axis at -3, 0, 2)
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name herman 1. first make like units, and then add. a. \\(\\frac{3}{4} …
a. $\frac{25}{28}$ b. $\frac{11}{8}$ c. $\frac{45}{56}$ d. $\frac{64}{63}$ e. $\frac{13}{15}$ (Note: Part f is incomplete and cannot be solved with the given information)
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for 5 - 16, find each sum. use a tool as needed. 5. $\frac{3}{12} + \fr…
$\frac{7}{12}$ ### Problem 6: $\boldsymbol{\frac{4}{10} + \frac{1}{10}}$
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mixed review how to add fractions how to multiply fractions $\frac{1}{5…
1. $\frac{13}{8}$ 2. $\frac{383}{42}$ 3. $\frac{20}{3}$ 4. $\frac{5}{3}$ 5. $\frac{3}{2}$
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25) ** solve: \\(\\log_{6}(x) + \\log_{6}(x - 9) = 2\\)
\(x = 12\)
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2. $y = \\frac{3}{4}x - 2$ | x | y | | -4 | | | 0 | | | 4 | | | 8 | | (…
| x | y | |----|----| | -4 | -5 | | 0 | -2 | | 4 | 1 | | 8 | 4 | To graph the line: plot the points (-4, -5), (0, -2), (4, 1), (8, 4) on the coordinate grid, then draw a straight …
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which trigonometric ratios are correct for triangle def? select three o…
- $\sin(D) = \frac{24}{25}$ - $\tan(D) = \frac{24}{7}$ - $\sin(E) = \frac{7}{25}$
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1. first make like units, and then add. a. $\frac{3}{4} + \frac{1}{7} =…
a. $\frac{25}{28}$ c. $\frac{45}{56}$ e. $\frac{13}{15}$
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e) what is the value of f(-5), if f(x) = -9x - 4? i) 41 ii) -49 iii) -4…
i) 41
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d) if $f(x) = -13 + 7x$ ; find the following. 1) $2f(8) + 7f(2)$ = ____…
s: 1) \( \boldsymbol{93} \) 2) \( \boldsymbol{\frac{39}{16}} \) (or \( 2.4375 \)) 3) \( \boldsymbol{-486} \) 4) \( \boldsymbol{-122} \)
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1) 2f(8) + 7f(2) = \\underline{\\qquad\\qquad} 2) \\frac{f(13)}{4f(3)} …
To solve these problems, we need the specific function \( f(x) \) or the values of \( f(8) \), \( f(2) \), \( f(13) \), \( f(3) \), \( f(1) \), \( f(-2) \), \( f(9) \), and \( f(0…
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a) evaluate each function at the specified value 1) $f(x) = 10x + 2 ; x…
\( f(-8) = -78 \) ### A) 2)
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graph the solution to the following system of inequalities. y<4x+5 y≥-3…
The solution is the region below the dashed line \( y = 4x + 5 \) and above the solid line \( y=-3x - 4 \) (graphically, this is the area where the shadings from both inequalities…
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Question was provided via image upload.
To solve these problems, we use the function \( f(x) = -x - 11 \) and substitute the given values of \( x \) into the function. ### 1) \( 4f(-2) + 5f(1) \) ## Step 1: Find \( f(-2…
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convert the fraction below into a decimal \\(\\frac{14}{15}\\) answer e…
The non - repeating part is 9 and the repeating part is 3, so the decimal is $0.\ 9\ \overline{3}$ (filling in the blanks: first blank 9, second blank $\overline{3}$)
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what are the domain and range of $f(x) = -37$? a domain: all real numbe…
D. Domain: All real numbers Range: \( \{ -37 \} \)
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find the inverse of the following function. $f(x) = 2x^3 - 5$ - $f^{-1}…
\( f^{-1}(x)=\sqrt[3]{\frac{x + 5}{2}} \) (the first option)
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what is the equation in slope - intercept form of the line that crosses…
D. \( y=\frac{9}{4}x - 81 \)
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graph this line using the slope and y-intercept: y = 7x - 8 click to se…
To graph \( y = 7x - 8 \): 1. Plot the y - intercept at \( (0,-8) \). 2. Use the slope \( 7\) (rise \( 7\), run \( 1\)) to find another point, e.g., from \( (0,-8) \), move right …
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determine the domain of the following graph:
$-1 \leq x \leq 8$ (or in interval notation: $[-1, 8]$)
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1 classify each graph or equation as a linear, quadratic, or exponentia…
### For \( y = \frac{1}{2}x - 5 \): ## Step1: Recall linear function form A linear function has the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - interc…
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6. accurately sketch the graph of the following functions (labeling imp…
- Domain: \( \boldsymbol{\{x\in\mathbb{R}:x eq - 4,x eq2\}} \) - Range: \( \boldsymbol{\mathbb{R}} \) - X - Intercept: \( \boldsymbol{(0,0)} \) - Y - Intercept: \( \boldsymbol{(…
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attributes of cubic and cube root functions the table below represents …
x - intercept(s): \((1, 0)\) y - intercept: \((0, -7)\) (corresponding to the option with x - intercept \((1,0)\) and y - intercept \((0, - 7)\))
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what is the equation in slope-intercept form of the line that passes th…
D. \( y =-\frac{5}{2}x + 3 \)
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question convert the fraction below into a decimal $dfrac{1}{6}$ answer…
0.1\(\overline{6}\) (where the non - repeating part is 1 and the repeating part is 6)
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40 how find the sum -0.25 - 1.5 = -0.25 + (-1.5) = \\boxed{}
\(-1.75\)
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mhf 4u0 - rehauhan 8. given the graphs of f(x) and g(x) as shown, find …
a) $(f \circ g)(1)=0$ b) $(f \circ f)(-2)=0$
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12. $-|-16| div \frac{(3^2 - 4)}{5 - 10}$
\(16\)
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9. what does the \downs system\ give the offensive team? * a) unlimited…
D) Four downs (plays) to move the ball past the line of scrimmage or score ### Question 10
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writing equations of linear functions use the given information in each…
### Individual Problem Results: 1. y-intercept: $0$, equation: $y = -\frac{1}{6}x$ 2. y-intercept: $5$, equation: $y = 2x + 5$ 3. y-intercept: $-2$, equation: $y = -7x - 2$ 4. y-i…
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5. determine the simplified linear function for $f(x)=\\frac{2x^2 - 15x…
The point of discontinuity is \((7, 13)\)
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10. \\(\\frac{17.5 - 3.5}{3^2 + 1}\\)
\(1.4\)
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find the product. \\(\\frac{2}{3} \\times 5 = 2 \\times \\frac{5}{3}\\)…
$\frac{10}{3}$ (or $3\frac{1}{3}$ as a mixed number)
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find the quotient. 5 ÷ 3 = ?
$\frac{5}{3}$ (or $1\frac{2}{3}$)
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9. \\frac{2^5 \\div 8 + 3}{4 + 3}
\(1\)
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which expression is equivalent to \\(\\frac{1}{3} \\times 5\\)? \\(5 \\…
$5 \div 3$
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9. (2³ + 8 + 3)/(4 + 3)
\(\frac{11}{7}\) (or \(1\frac{4}{7}\))
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use the graph of f(x) to complete the table. (graph of a piecewise func…
| $x$ | $f(x)$ | |-----|--------| | -5 | -3 | | 2 | 1 | | 10 | 5 |
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use the following function rule to find f(8). f(x) = \\frac{40}{x} + 5 …
10
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use the following function rule to find f(0). f(x) = 6^x + 1 f(0) = sav…
2
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use this graph of f to find the solution to f(x) = -6.
$x=4$
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9×7=__ __×__=__ __÷__=__ __÷__=__
\( 9 \times 7 = \boldsymbol{63} \) \( \boldsymbol{7} \times \boldsymbol{9} = \boldsymbol{63} \) \( \boldsymbol{63} \div \boldsymbol{7} = \boldsymbol{9} \) \( \boldsymbol{63} \div …
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use the graph of g(x) to complete the table. graph of g(x) with grid, a…
| $x$ | $g(x)$ | |-----|--------| | $-9$ | $9$ | | $-6$ | $6$ | | $10$ | $-7$ |
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Question was provided via image upload.
The equation of the line is \(y=x - 2\)
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4 × 10 = 40 __×__=__ __÷__=__ __÷__=__
\( 4 \times 10 = \boldsymbol{40} \) \( 10 \times 4 = 40 \) \( 40 \div 4 = 10 \) \( 40 \div 10 = 4 \)
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3 × 6 = 18 __×__=__ __÷__=__ __÷__=__
$3 \times 6 = \boldsymbol{18}$ $6 \times 3 = 18$ $18 \div 3 = 6$ $18 \div 6 = 3$
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use this graph of g to find the solution to g(x) = 5.
$x=-9$ and $x=7$
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evaluate the diagram and answer the question below. limits the presiden…
2.6) C. War Powers Resolution 2.7) B 2.8) H 2.9) S 2.10) S 2.11) H 2.12) B 2.13) S 2.14) B 2.15) H
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the graph of $y = \\sqrt{x}$ is shown on the grid below. graph of y = s…
B. (The graph of option B)
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use the following function rule to find f(-7). f(x) = x² - 4x f(-7) = s…
77
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use this graph of f to find f(-4).
2
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evaluate the diagram and answer the question below. limits the presiden…
2.6) C. War Powers Resolution 2.7) B 2.8) H 2.9) S 2.10) S 2.11) H 2.12) B 2.13) S 2.14) B 2.15) H
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use the following function rule to find f(81). f(x) = -6 + \\sqrt{x} f(…
3
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function $f$ is graphed. graph of a function f on a coordinate plane wi…
A. Even
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fill in the blanks. to solve exponential and logarithmic equations, you…
\(x = y\) ### Part (b)
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3 true or false 1 point children are only aware of print in the environ…
3. False 4. False 5. A. inviting and cozy.
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the graph of $y = g(x)$ is a transformation of the graph of $y = f(x)$.…
$g(x) = \sqrt{x + 4} + 4$
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function g is defined as $g(x) = -f(-x)$. what is the graph of g? choos…
B. (The graph of option B)
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function f is graphed. graph of a function f on a coordinate plane with…
B. Odd
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7. - / 1 points solve for x. ln x - ln 8 = 0 x = resources read it subm…
$x = 8$ ### Problem 8
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function g is defined as $g(x) = \\frac{1}{2}f(x)$. what is the graph o…
C
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functions $f$ (solid) and $g$ (dashed) are graphed. graph of two functi…
B. \( g(x)=-f(x) \)
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the graph of $y = g(x)$ is shown on the grid below. graph of y = g(x) w…
C (assuming the option C is the graph with the correct shift, but based on the transformation rules, the graph of \( y = g(x - 4)-2 \) is the graph of \( g(x) \) shifted 4 units t…
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determine whether each x - value is a solution (or an approximate solut…
(a) A. Yes (b) B. No Wait, but let's confirm again. For part (a): Given $\log_{3}(x + 3)=7$. Convert to exponential form: $x + 3=3^{7}$. Calculate $3^{7}=2187$. Then $x=2187 - 3=2…
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choice below and fill in any answer boxes within your choice. a. $\tan …
A. $\tan 120^{\circ}=-\sqrt{3}$
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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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question 7 (mandatory) (1 point) determine the roots of $3.3x^2 + 1.9x …
d) -1.19 and 0.61
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imagine 6 in your head double it add 3 write the tens digit. a imagine …
1 ### Second Box (B and C)
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6. * which graph represents the system of equations? ( y = \frac{2}{3}x…
C
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question 1 (1 point) compare the graph to the absolute value parent fun…
a. Reflected over the x - axis, d. Vertical Shift Up
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question 16 (1 point) compare the equation to the absolute value parent…
d. Vertical Shift Up, g. Graph is Wider
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synthetic division table -21 | -4 -86 -47 -105 -3 -63 84 42 105 0 63 -4…
0
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question 15 (1 point) compare the equation to the absolute value parent…
b. Horizontal Shift Left f. Graph is Narrower
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compare the equation to the absolute value parent function ($y = |x|$).…
b. Horizontal Shift Left d. Vertical Shift Up
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question 13 (1 point) compare the equation to the absolute value parent…
a. Reflected over the x - axis
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compare the equation to the absolute value parent function ($y = |x|$).…
b. Horizontal Shift Left d. Vertical Shift Up
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3\\overline{) 36}
The result of \( 36 \div 3 \) is 12.
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synthetic division table -21 | -4 -86 -47 -105 -3 -63 84 42 105 0 63 -4…
0
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question 11 (1 point) compare the equation to the absolute value parent…
b. Horizontal Shift Left
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compare the graph to the absolute value parent function ($y = |x|$). se…
b. Horizontal Shift Left, e. Vertical Shift Down
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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 1 (1 point) compare the graph to the absolute value parent fun…
a. Reflected over the x - axis, d. Vertical Shift Up
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compare the graph to the absolute value parent function ($y = |x|$). se…
b. Horizontal Shift Left, 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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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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subtract. \\(\\frac{8}{10} - \\frac{3}{5} = \\square\\) use the model t…
$\frac{1}{5}$ (or $\frac{2}{10}$)
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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