微积分
极限、导数、最优化与函数性质。
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the graph of $y = 2^x$ is shown below. which of the following is the gr…
A. <The graph with horizontal asymptote $y=4$, decreasing, passing through $(0,-4)$>
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given $f(x) = \\sqrt{x}$ and $g(x) = x + 4$, find $(f \\circ g)(x)$.$\\…
$\boldsymbol{f(x) = \sqrt{x+4}}$ (the fourth option)
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which graph could be the inverse of $f(x)$? a b c none of these
B
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a true statement about credit card fees and interest rates is if a pers…
B. a credit card issuer can raise the interest rate if a person has a pattern of being late in paying another creditor.
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given $f(x) = \\sqrt3{x}$ and $g(x) = x^3 - 3x + 10$, find $(f \\circ g…
2
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$y = \\frac{1}{x}$ what is true about the given function? ○ the end beh…
All of these are correct.
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during which interval is the graph of the function below only increasin…
1. d. $-2 < x < \infty$ 2. b. $x = 5$
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which function is best represented by this graph? https://flic.kr/p/2ov…
a. $f(x) = \frac{5}{x+3}$
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the graph of a function is shown below. which family could this functio…
d. Cube Root
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when can a person continue to charge credit card purchases beyond his c…
If the person opted in for over-the-limit fees.
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7) $y < |x - 5|$ $2x - y > 1$
The solution is the overlapping shaded region below both the dashed V-shaped graph $y=|x-5|$ and the dashed line $y=2x-1$, bounded by their intersection at $(2, 3)$.
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7) $y < |x - 5|$ $2x - y > 1$ 8) $y < |x - 2|$ $y > 2x - 4$ 9)
### For Problem 7: - The solution is the overlapping shaded area below the dashed V-shaped graph $y=|x-5|$ and below the dashed line $y=2x-1$, with the boundary intersection at $(…
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find the inverse function of the function $f(x)=3x-7$. answer $\bigcirc…
$f^{-1}(x) = \frac{x+7}{3}$
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question find the inverse function of the function $f(x)=8x - 9$. answe…
$\boldsymbol{f^{-1}(x) = \frac{x+9}{8}}$ (corresponding to the first option in the answer choices)
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find the inverse function of the function $f(x)=\\frac{1}{5}x - 5$. ans…
$f^{-1}(x) = 5x + 25$
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how do the coordinates of a function and its inverse relate to each oth…
They are swapped
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what does the line $y = x$ represent in the context of inverse function…
The axis of symmetry for the inverse
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what is the inverse of the function $f(x) = x^3$? options: $3x$ $3 \\ti…
The cube root of x
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what is the graphical representation of an inverse function primarily c…
4. Reflection over the line $y=x$
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jamarion bruce q3 - accelerated mathematics gr 8 | guided notes: writin…
1. problem context 2. variables 3. quantities 4. $\geq$ 5. $\leq$ 6. rewrite 7. $\leq$
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11. write a rule for $g$ that represents the indicated transformations …
$6\log_{6} x - 5$
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select all that apply which of the following are effective annotation t…
B. identifying terms explicitly defined in the text C. circling or noting unfamiliar terms and writing out definitions D. including your reactions and questions in the margin
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warm-up (7 minutes)find the key features of the function f(x) here1. do…
1. Domain: All real numbers, or $(-\infty, \infty)$ 2. Range: All real numbers, or $(-\infty, \infty)$ 3. X-intercept: $(0, 0)$ 4. Y-intercept: $(0, 0)$ 5. Minimum: None 6. Maximu…
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what does the notation $f^{-1}(x)$ represent? 1. the function raised to…
4. The inverse of the function f(x)
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determine the slope and y-intercept for this relationship. round to the…
750
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first, complete the following table. use only integer values. x y 0 6 5…
m: 8 b: 6 Equation: $y=8x+6$
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09 february 2025 calculate with integer 1.) calculate a.) $-52 + 16$ b.…
1.) a) $-36$ 1.) b) $-308$ 1.) c) $260$ 2.) a) $587$ 2.) b) $-71$
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1.1 - solving quadrativalue: 6solve the quadratic by taking square root…
x=7,-7
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select the correct answer. find the value of $h(-67)$ for the function …
C. 3,158
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look at this graph: what is the y-intercept?
5
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$f(x) = \\frac{3}{2}x + 4$ using the given function, plot all the order…
The ordered pairs to plot are: $(-8, -8)$, $(-4, -2)$, $(-2, 1)$, $(0, 4)$, $(2, 7)$, $(4, 10)$
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write the equation of a function $g(x)$ whose graph is the graph of $f(…
$g(x) = \boldsymbol{\frac{1}{2}}|x \boldsymbol{-} \boldsymbol{6}| \boldsymbol{+} \boldsymbol{4}$
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graph $h(x) = -2|x + 5| - 3$.
The graph is a downward-opening V with vertex at $(-5, -3)$, passing through points such as $(-4, -5)$ and $(-6, -5)$.
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function analysis comparing shapes of functions click for long desc sel…
Option #2: The graph of the function matches $f(x) = \sqrt{x}$.
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function analysis > comparing shapes of functions click for long desc c…
Option #1. The graph of the function matches $f(x) = \sqrt[3]{x}$.
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** this is a 2-page document ** directions: graph each equation. show a…
1. Line for $y=-\frac{7}{4}x+1$: passes through $(0,1)$ and $(4,-6)$ 2. Line for $y=\frac{1}{3}x+4$: passes through $(0,4)$ and $(3,5)$ 3. Line for $y=-x-3$: passes through $(0,-3…
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given functions $f(x)$ and $g(x)$ shown below:$f(x)=\\begin{cases}x^2+5…
A. $9$ B. $6$ C. $15$
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given functions $f(x)$ and $g(x)$ shown below $f(x)=\\begin{cases}x^{2}…
A. $f(5)=-15$ B. $g(8)=-8$ C. $2f(5)-g(8)=-22$
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use technology to graph the function in order to answer the question be…
Positive: $(-\infty,-3)$ Increasing: $(-1,4)\cup(4,5)$ Negative: $(-3,5)$ Decreasing: $(-\infty,-1)$
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u1 assessment wchs let $f(x)=2(x-5)^2+3$ for what restricted domain wou…
$x \geq 5$ OR $x \leq 5$
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what are the domain and range of $f(x) = 4^x - 8$? ○ domain: {x | x is …
domain: $\{x \mid x \text{ is a real number}\}$; range: $\{y \mid y > -8\}$
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which graph represents the function $y = 2x - 4$?
The third graph (rightmost top graph, passing through $(0,-4)$ and $(2,0)$ with a steep positive slope)
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which graph represents the function $g(x) = |x + 4| + 2?$
The first graph (leftmost graph, with vertex at $(-4, 2)$)
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the graph shows the function $f(x) = (2.5)^x$ was horizontally translat…
-2
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what is the inverse of the function $f(x) = 4x + 8$? $h(x) = \\frac{1}{…
A. $h(x) = \frac{1}{4}x - 2$
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the inverse of the function $f(x) = \\frac{1}{2}x + 10$ is shown. $h(x)…
D. 20
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what are the domain and range of the function $f(x) = 4(\\sqrt3{81})^x$…
$\{x| x \text{ is a real number}\}; \{y| y > 0\}$
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which is the graph of $y - 3 = -\frac{2}{3}(x + 6)$?
The first graph (with points $(-3,1)$, $(0,-1)$, $(3,-3)$)
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gina wants to take dance classes. she compares two dance studios to det…
10
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the function graphed is reflected across the x-axis to create a new fun…
The domain stays the same, but the range changes.
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type the correct answer in each box. use numerals instead of words. wha…
$(0, -22)$
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select the quadratic function with a graph that has the following featu…
B. $f(x) = -x^2 + 12x - 32$
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find the vertex of the quadratic function given below. $f(x) = (x - 4)(…
A. (1,-9)
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2) $y = -\frac{5}{2}x + 4$
The line $y=-\frac{5}{2}x+4$ is graphed by plotting the points $(0, 4)$ and $(2, -1)$ and drawing a straight line through them, extending across the provided coordinate grid.
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what is the range of the function $f(x) = -2|x + 1|$? all real numbers …
all real numbers less than or equal to 0
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find the inverse of $f$. $f(x)=x^3 - 5$ $\bigcirc \\ f^{-1}(x)=\\sqrt3{…
$f^{-1}(x) = \sqrt[3]{x + 5}$ (the last option)
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let $f(x)=4x^{2}+\\sqrt{-5x}$ evaluate $f(-5)$ -405 none -95 -395 105
105
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consider the function $y = a\\sin(bx)$, where $a > 0$ and $b > 0$. whic…
Decrease a.
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consider the function $y = a\\cos(bx)$, where $a > 0$ and $b > 0$. whic…
Decrease b.
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which graph represents the function $y = -2\\cos(2\\pi x)$?
The third graph (left-to-right, bottom-right of the four) which has amplitude 2, period 1, starts at $(0,-2)$ and completes a full cycle every 1 x-unit.
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graphing sine and cosine functions what is one characteristic of the co…
Its graph is symmetric about the y-axis.
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on the interval $0 \\leq x \\leq 2\\pi$, what are the $x$-intercepts of…
0, $\pi$, and $2\pi$
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the function $f$ is defined by $f(x)=2^{x}$.which of the following stat…
When the input $x$ increases by 1, the value of $f$ increases by a factor of 2. When the input $x$ increases by 3, the value of $f$ increases by a factor of 8.
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whenever the input of a function $f$ increases by 1, the output increas…
\(f(x) = 5x + 3\)
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article i_______ branchcongress _______ laws._______how many? __qualifi…
### Article I (Legislative Branch) - **Article I: Legislative branch** - **Congress makes laws.** - **House of Representatives** - How many?: 435 - Qualifications: At least 25 yea…
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determine whether the function, $f(x) = -4x + 7$, is invertible ○ inver…
invertible $f^{-1}(x) = \frac{7 - x}{4}$
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which of the following statements are true? choose three correct answer…
- The graph is stretched vertically by a factor of 5. - The graph is stretched horizontally by a factor of 2. - The period is $4\pi$.
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describe the x-values for which the function is increasing, decreasing,…
The function is increasing when \(x < -1.15\) and \(x > 1.15\) and decreasing when \(-1.15 < x < 1.15\). The function is positive when \(-2.00 < x < 0.00\) and \(x > 2.00\), and n…
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|x|y|| ---- | ---- || $-\frac{pi}{2}$ | 0 || 0 | 6 || $\frac{pi}{2}$ | …
- The maximum value of the function is 6. - The frequency is $\frac{1}{2\pi}$. - The function increases on the interval $(\pi, 2\pi)$.
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which graph represents a function with amplitude 4 and period $pi$?
The third graph (left-to-right, the one with amplitude 4 and period $\pi$)
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a cosine function has been reflected over the $x$-axis and horizontally…
$y = -\cos(3x)$
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analyzing a sine graph which of the following statements are true? choo…
The amplitude is $\frac{1}{2}$. The equation of the graph is $y = \frac{1}{2}\sin(2x)$ The graph is compressed horizontally by a factor of $\frac{1}{2}$
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analyzing a sine graph which of the following statements are true? choo…
# Explanation: ## Step1: Identify amplitude The amplitude is the maximum vertical distance from the midline. From the graph, the peak is at $y=2$, so amplitude is $2$. ## Step2: C…
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① $y=\\frac{1}{3}x + 3$
The graph is a straight line passing through points $(0, 3)$ and $(2, 4)$, extending infinitely in both directions.
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which graph represents the equation $y = 3\\sin\\left(\\frac{1}{3}x\ ig…
The first graph (left-most graph with amplitude 3 and period $6\pi$)
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which domain window settings would be appropriate if you wanted to grap…
X min = -90 X max = 270
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listen find the inverse of $f(x)=\\frac{1}{3}x - 2$. the inverse is $g(…
$g(x)=3x+6$ ### Graphing Notes (for reference): 1. For $f(x)=\frac{1}{3}x-2$: Plot the y-intercept $(0, -2)$, then use slope $\frac{1}{3}$ (rise 1, run 3) to find another point li…
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use a graphing calculator to solve $4x^{2}+x=\\frac{1}{2}x^{4}+1$ by gr…
B) -1.93, E) -0.13, G) 0.39, I) 2.91
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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.