Calculus
Limits, derivatives, optimization, and behavior of functions.
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nalyzing a cosine graph here is the graph of a cosine function in the f…
- The period is $\pi$ - The graph is stretched vertically by a factor of 2 - The graph is horizontally compressed by a factor of $\frac{1}{2}$
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working with radicals complete the table below. each expression should …
| Written in radical notation | Written using rational exponents | Evaluated to two decimal places | |------------------------------|-----------------------------------|----------…
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solving equations with fractional exponents score: 5/10 penalty: none q…
$531441$
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find the slope of each line and write the equation of each graph. 9. 10.
Slope: \(-\frac{1}{5}\), Equation: \(y =-\frac{1}{5}x - 2\) ### Problem 10
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review passage find the sine and cosine of the given angle question 210…
$\cos(210^{\circ}) = -\frac{\sqrt{3}}{2}, \sin(210^{\circ}) = -\frac{1}{2}$
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given $f(x) = \\frac{4x - 7}{8x + 8}$, what is the end behavior of the …
As \( x \to -\infty \), \( f(x) \to 0.5 \); as \( x \to \infty \), \( f(x) \to 0.5 \). (The corresponding option from the choices, e.g., if the first option is "As \( x \to -\inft…
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given $f(x)=\frac{2}{x^2 + 3x - 10}$, which of the following is true? $…
f(x) is positive for all \(x < -5\) (the first option)
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select the correct answer. given that a function, g, has a domain of -2…
D. \( g(-13) = 20 \)
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type the correct answer in each box. use numerals instead of words. if …
For the first box (when $-3 \leq x < -1$): $x + 3$ For the second box (when $-1 \leq x \leq 1$): $5$ So the piecewise function is: $f(x) = \begin{cases} \boldsymbol{x + 3}, & \tex…
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what is the range of the function shown on the graph above? a. $-2 \\le…
D. \(-9\leq y\leq8\)
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select the correct answer from each drop down menu. let d(t) be the tot…
For \( d(4) \), we substitute \( t = 4 \) into \( d(t)=12t + 20 \): \( d(4)=12\times4 + 20=48 + 20 = 68 \) So \( d(4)=\boldsymbol{68} \). This means that after \(\boldsymbol{4}\) …
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find the value of h(-7) for the function below: h(x) = 5.7 - 19x a. 0.6…
B. 138.7
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use the drawing tools to form the correct answer on the graph. graph th…
# Explanation: ## Step1: Identify the y-intercept The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-5x + 3\), when …
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question 3 (5 points) (01.04 mc) which of the following is an example o…
d. The lyrics to a song ### Question 4
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find an equation of the tangent line to the graph of $y = g(x)$ at $x =…
$y = 2x-14$ (or $y+4 = 2(x - 5)$ or $2x-y-14=0$, but the slope - intercept form $y = 2x-14$ is a standard answer)
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use the graph of f(x) below to put the values of f(-6), f(0), and f(4) …
\( f'(0) > f'(4) > f'(-6) \) (which corresponds to the option: \( f'(0) > f'(4) > f'(-6) \))
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find the horizontal and vertical asymptotes of the curve. $y = \\frac{4…
### First Problem: Find Horizontal and Vertical Asymptotes of \( y = \frac{4x^2 + x - 5}{x^2 + x - 12} \) #### Vertical Asymptotes (Step 1: Factor Denominator) To find vertical as…
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hw 2.3 functions and relations question 13 of 15 (2 points) | question …
### Part (a): Determine \( f(-5) \) ## Step 1: Identify the point on the graph We look for the point with \( x = -5 \) on the graph of \( y = f(x) \). From the graph, the point \(…
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hw 2.8 algebra of functions and function compositions question 14 of 17…
\(-\pi^2 + 4\pi + 2\)
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question 5 1 pts one feature of state tax codes that has traditionally …
C. 40%
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monday substitution. what is the value of y if x = 4? \\( y = 5x + 12 \…
1. For $y=5x+12$ when $x=4$: $y=32$ 2. For $y=\frac{3}{2}x-10$ when $x=4$: $y=-4$ 3. True equation: c) $y=-5x+20$ 4. For $3x-5=7-x$: 1 solution, $x=3$
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question 5 (5 points) listen which colony did not attend the first cont…
Question 5: B. Georgia Question 6: A. It stated that the central government wouldn't control western lands.
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perform the indicated operation $7\\frac{1}{8}-2\\frac{2}{3}$ $7\\frac{…
\(4\frac{11}{24}\)
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the function ( f ) is continuous on the closed interval (2,8) and has v…
C. 160 ### Second Problem (Tangent Line)
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question 20 consider the function $h(x) = -2x^2 + 20x - 51$ graph $h(x)…
- Vertex of $h$: $(5, -1)$ - Equation of the line of symmetry: $x=5$ - $h$ has a maximum of $-1$ - The $x$-intercept(s) of $h$: None (no real intercepts) - The $y$-intercept of $h…
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evaluate the function for the given values of x. \\( g(x)=\\begin{cases…
\( -13 \) ### Part 2: \( g(5) \)
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evaluate the function for the given values of x. $g(x)=\\begin{cases} -…
\( 6 \) ### Part 2: \( g(-2) \)
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part 1 of 3 (a) given ( f(x) = -x^4 + 4|x| ), find ( f(-x) ). ( f(-x) =…
\( f(-x) = -x^4 + 4|x| \) ### Part 2 of 3
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use the quadratic formula to solve the equation $25x^2 - 50x + 36 = 0$.…
$1+\frac{\sqrt{11}}{5}i, 1-\frac{\sqrt{11}}{5}i$
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here is an equation. 2x - 1 = 5 draw a graph to help solve the equation…
\(x = 3\)
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8. (u5 l11 p1) select all expressions that are equal to $\\log_{2}8$. a…
### Question 8 First, calculate \( \log_{2}8 \): ## Step 1: Simplify \( \log_{2}8 \) We know that \( 2^3 = 8 \), so by the definition of logarithms (\( \log_{a}b = c \) means \( a…
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question 2.2 give the quadratic graphed below identify the vertex of th…
Vertex: $(-2, 2)$; Equation: $y = -2(x + 2)^2 + 2$ Vertex: $(-1.8, -22.1)$; $a = 2$; Vertex-form: $m(x) = 2(x + 1.8)^2 - 22.1$
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12. what bias might exist in mr. payne’s testimony as a coal master? a.…
B. He benefits from defending mine conditions ### Question 13
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hw 2.7 analyzing graphs and piecewise-defined functions question 6 of 1…
When we replace \( x \) with \( -x \) and \( y \) with \( -y \) in \( y = x^2+8x + 3 \), we get \( -y=(-x)^2+8(-x)+3\), which simplifies to \( -y=x^2 - 8x + 3 \), and then \( y=-x…
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the population of the united states and canada is distributed very diff…
The population of the United States and Canada is distributed very differently. The United States has a population of over **334** million people distributed across many regions. …
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23. the old woman offers a lengthy rebuttal to the knight’s complaints.…
23. To shift the power dynamic and establish the old woman's moral and intellectual authority, reinforcing the theme of female sovereignty. 24. Yes; she teaches him that true nobi…
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an adjective is a word that modifies a noun or a pronoun. example: he l…
1. mountains: snow-capped, towering, rocky 2. weather: sunny, chilly, stormy 3. journey: tedious, exciting, scenic 4. classroom: spacious, noisy, bright 5. book: thrilling, tatter…
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determine the arc length ( l ) of the curve defined by the equation ( y…
$144 - \frac{4\sqrt{2}}{3}$
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read the excerpt and answer the question that follows: \veto of the war…
C. Congress wanted to limit the president’s power to send U.S. troops into armed conflicts.
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the graph of $f$, the derivative of $f$, is shown in the graph below. i…
\( \boxed{-2} \)
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the functions f and g are defined as follows. \\( f(x) = -4x + 2 \\) \\…
\( f(6)=\boxed{-22} \) \( g(-2)=\boxed{18} \)
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question write the equation of the trigonometric function shown in the …
\( y = 2\cos(x) \)
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the graph of a function ( h ) is shown below. find ( h(2) )
\( h(2)=1 \)
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the graph of a function ( h ) is shown below. find ( h(2) ). ( h(2)=squ…
\( \boxed{0} \)
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the graph of a function ( h ) is shown below. find ( h(1) ). ( h(1)=squ…
\( h(1) = 5 \)
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find the slope of the line passing through the points (-2, 8) and (-9, …
\(\frac{3}{7}\)
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below is the graph of $f(x)=\\sqrt{x}$. transform it to make it as the …
First, shift the graph of \( f(x)=\sqrt{x} \) 2 units to the left, then shift the resulting graph 4 units down to obtain the graph of \( g(x)=\sqrt{x + 2}-4 \).
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find the slope of the line passing through the points (3, 4) and (8, -3…
\(-\frac{7}{5}\)
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use translations to graph the given function. $g(x)=\\sqrt{x + 2}-4$ yo…
s for Part 3: - The point \( (0,0) \) on \( f(x) \) corresponds to \( (-2,-4) \) on \( g(x) \). - The point \( (1,1) \) on \( f(x) \) corresponds to \( (-1,-3) \) on \( g(x) \). -…
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compute. -11.6 + 8 + 8.3
4.7
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compute. 3.6 - 7 - 1.3
-4.7
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compute. 2 - 8.3 + 3.8
$-2.5$
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cos 30° answer \\(dfrac{sqrt{3}}{2}\\) \\(dfrac{sqrt{2}}{2}\\) \\(dfrac…
$\frac{\sqrt{3}}{2}$
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attempt 1: the answer is incorrect. 9 attempts remaining. suppose ( c(x…
\( 355.90 \)
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9 longdiv 6320
# Explicación: ## Paso 1: Dividir los primeros dígitos Calculamos cuántas veces 19 cabe en 63: $19 \times 3 = 57$. Restamos: $63 - 57 = 6$. ## Paso 2: Bajar el siguiente dígito Ag…
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attempt 1: 10 attempts remaining. a carpenter is building a rectangular…
Side length (both length and width, since it's a square): \( 10.5 \) feet Maximum area: \( 110.25 \) square feet
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suppose the position of a particle, s(t) is given by s(t)=t²−8t+30 feet…
\( v(t)=2t - 8 \) ### Part (b)
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use the graph, given above, to find the slope of each line. a) slope of…
Slope of Line 2 (red) = $-\frac{1}{2}$
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attempt 3: 8 attempts remaining. morgan wants to enclose an outdoor rec…
- Side length opposite the house: \( \boldsymbol{55} \) feet - Side length perpendicular to the house: \( \boldsymbol{27.5} \) feet - Maximum area: \( \boldsymbol{1512.5} \) squar…
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what is the quotient of 11,310 ÷ 26? 435 \\(\frac{20}{26}\\) 435 430 33…
B. 435
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multiply 14.3 ×1.76 ————
25.168
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find 5.55 × 6.4. 5.55 × 6.4 = \\square
\(35.52\)
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question 1-5 what is 10,296 ÷ 66?
156
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find the product. 21.6•2.1 21.6•2.1 = (type an integer or a decimal.)
45.36
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what is the quotient of 13,756 ÷ 15? 1,583 \\frac{11}{15} 971 \\frac{1}…
C. \(917\frac{1}{15}\) (assuming the third option is labeled C, if the original options have labels like A, B, C, D with the third being C for \(917\frac{1}{15}\))
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4 ÷ x × \\frac{9}{10} =
$\frac{15}{4}$ or $3\frac{3}{4}$
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Question was provided via image upload.
\( (4, -4) \), Sum of \( x \& y \): \( 0 \) ### Problem 2: Solve the system \( y = 3x + 18 \) and \( y = -\frac{1}{2}x - 17 \)
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why is there limited agriculture in eastern europe? lack of native farm…
C. Lack of proper soils and favorable climates ### Second Question (How are Southern Appalachian (U.S.A) and Southwestern Caucasus (Russia) forests similar?)
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which of the following best compares how the chinese exclusion act and …
C. Both laws targeted specific groups through either exclusion or quotas to limit immigration. ### Second Question
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choose the best answer to complete the statements. the graph of $f(x)$ …
1. The graph of $f'(x)$ is Graph B 2. The graph of $g'(x)$ is Graph A 3. The graph of $h'(x)$ is Graph D
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choose the best answer to complete the statements. $f(x)$ the graph of …
1. The graph of $f'(x)$ is: Graph B. A downward-sloping straight line through the origin 2. The graph of $g'(x)$ is: Graph D. A decreasing, concave-down curve below the x-axis 3. …
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choose the best answer to complete the statements. the graph of $f(x)$ …
1. The graph of $f'(x)$ is Graph D 2. The graph of $g'(x)$ is Graph B 3. The graph of $h'(x)$ is Graph A (correct as selected)
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consider the following function. $y = 4x - 3$ complete the value in the…
$a=-11$
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julie went hiking with her friends. the graph shows the distances they …
4
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the point $(-3, 6)$ is on the graph of the function $f(x) = -6sqrt3{x +…
### Part (a) | Interval | Average rate of change | |-------------------|------------------------| | $[-3.1, -3]$ | $-1.9368$ | | $[-3.01, -3]$ | $-1.9934$ | | $[-3.001, -3]$ | $-1…
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the point $(-5, 8)$ is on the graph of the function $f(x) = -dfrac{8}{4…
### Part (a) | Interval | Average rate of change | |-------------------|------------------------| | $[-5.1, -5]$ | $7.2727$ | | $[-5.01, -5]$ | $7.9208$ | | $[-5.001, -5]$ | $7.99…
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480\ × 13\ ———
6240
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the point (3, 1) is on the graph of the function $f(x) = -(x - 4)^3$ as…
### Part (a) | Interval | Average rate of change | |----------------|------------------------| | $[2.9, 3]$ | $-3.3100$ | | $[2.99, 3]$ | $-3.0301$ | | $[2.999, 3]$ | $-3.0030$ | …
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(\frac{296}{56} - \frac{350}{56})
$\frac{23}{28}$ (or the decimal equivalent $0.821$ rounded to three decimal places)
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the point (4, 9) is on the graph of the function $f(x) = 4sqrt{x} + 1$ …
(a) | Interval | Average rate of change | |----------------|------------------------| | $[3.9, 4]$ | 1.0064 | | $[3.99, 4]$ | 1.0010 | | $[3.999, 4]$ | 1.0000 | | $[4, 4.001]$ | 1…
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3\\frac{4}{6} + 2\\frac{6}{8}
$6\frac{5}{12}$ (or $\frac{77}{12}$)
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ook at another problem. evaluate -16 · 6. -16 · 6 =
-96
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evaluate 14 · -4. 14 · -4 =
\( -56 \)
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evaluate $14\\cdot\\frac{1}{2}$. $14\\cdot\\frac{1}{2}=\\square$
7
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evaluate 6·5. 6·5=□
30
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the point ((1, -8)) is on the graph of the function (f(x) = -\frac{8}{x…
### Part (a) | Value of $x$ | Slope | |--------------|-------| | 0.8 | 10.0000 | | 0.9 | 8.8889 | | 0.99 | 8.0808 | | 0.999 | 8.0080 | | 1.001 | 7.9920 | | 1.01 | 7.9208 | | 1.1 |…
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use the shell method to write and evaluate the definite integral that r…
$576\pi$
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the point $(-5, 8)$ is on the graph of the function $f(x) = -dfrac{8}{4…
### Part (a) Slopes (rounded to 4 decimals): | Value of $x$ | -5.2 | -5.1 | -5.01 | -5.001 | -4.999 | -4.99 | -4.9 | -4.8 | |--------------|------|------|-------|--------|--------…
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use the shell method to find the volume of the solid generated by revol…
$\frac{16\pi}{3}$
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use the graph to complete each of the following parts. (a) from the cho…
(a) None (b) $x=-2$, $x=2$ (c) $x=-3$, $x=0$, $x=3$ (d) $x=-3$, $x=-2$, $x=0$, $x=2$, $x=3$
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evaluate the definite integral. \\(\\int_{-1}^{1} (9x^2 + 6x - 3) dx = …
\(0\)
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question graph the following function on the axes provided. $f(x)=\\beg…
To graph the function: - For \( y = 4x + 17 \) ( \( x < -3 \) ): Plot an open circle at \( (-3, 5) \), then draw a line through points like \( (-4, 1) \), \( (-5, -3) \) (calculat…
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graph of h(x) answer \\( f(x) \\), \\( g(x) \\), \\( h(x) \\) \\( f(x) …
h(x), f(x), g(x) (the option: \( h(x), f(x), g(x) \))
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put the following functions in order of smallest minimum value to large…
The order from smallest minimum value to largest minimum value is \( f(x) \), \( g(x) \), \( h(x) \)
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use the graph given above, to find the slope and equation for the line.…
a) $1$ b) $y=x+1$
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the graph of ( f ) is shown in the figure below. on the same set of axe…
The graph of $f'(x)$ consists of two horizontal segments: 1. A horizontal line at $y=\frac{11}{4}$ (or 2.75) spanning the open interval $(-4, 0)$ 2. A horizontal line at $y=-1$ sp…
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order the following graphs by increasing slope of the line being displa…
Slope $\boldsymbol{A}$ < Slope $\boldsymbol{D}$ < Slope $\boldsymbol{C}$ < Slope $\boldsymbol{B}$
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for a function g, suppose we know the following. g(2) = -4, \\quad g(2)…
$y = 1.5x - 7$ (or equivalent point-slope form $y + 4 = 1.5(x - 2)$)
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suppose $y = -2x - 4$ is the equation of the tangent line to the graph …
$g(-1.5) = -1$ $g'(-1.5) = -2$
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3) graph $y = 2(x - 5)^2 - 6$
To graph \( y = 2(x - 5)^2 - 6 \): 1. Plot the vertex \((5, -6)\). 2. Draw the axis of symmetry \( x = 5 \). 3. Plot the points \((4, -4)\), \((6, -4)\), \((3, 2)\), \((7, 2)\) (a…