微积分
极限、导数、最优化与函数性质。
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which statement correctly explains whether the equation $y = x^2 - 2$ r…
B. It is a function because there is only one y-value for each x-value
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1. both of these functions grow as x gets larger and larger. which func…
$f(x)=4^x - 5$ eventually exceeds $g(x)=5x$ as $x$ gets larger. --- ### Second Question:
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find $\frac{h(8)}{f(-3)}$ in simplified form. $f(x)$ $g(x) = -x^2 + 3x …
$-\frac{3}{2}$
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the graph of the parent quadratic function $f(x)=x^{2}$ and that of a s…
The value of $a$ is less than -1, meaning $a < -1$.
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the graph of $y = f(x)$ is shown below. according to the graph, what is…
-1
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look at this graph: what is the minimum value of this function?
0
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given the function $f(x)=\\frac{1}{2}\\sqrt{x}$, use f(g(x)) to verify …
The function $g(x)$ is not the inverse of $f(x)$ because $f(g(x))$ is $|x|$ (not equal to $x$ for all $x$ in the domain of $f(x)$).
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list the interval(s) on which f is decreasing.the interval(s) on which …
$[-10, -8], [0, 2], [6, 8]$
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look at this graph: what is the minimum value of this function?
$-8$
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look at this graph: what is the y-intercept?
$0$
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question simplify the expression below using order of operations. $4^{2…
9
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write the equation of a sine function with amplitude = 7 and period = $…
$y = 7\sin(x)$
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look at this graph: what is the maximum value of this function?
10
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look at this graph: what is the maximum value of this function?
4
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write an equation for the function graphed below $y =$ question help: v…
$y = \frac{12(x-2)}{(x+3)(x-4)}$ (or expanded form $y = \frac{12x - 24}{x^2 - x - 12}$)
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look at this graph: what is the minimum value of this function?
-9
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look at this graph: what is the maximum value of this function?
0
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look at this graph: what is the minimum value of this function?
$-1$
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look at this graph: what is the maximum value of this function?
10
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find the range of the quadratic function. $y=2x^{2}+8x+5$ write your an…
$y\geq -3$
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look at this graph: what is the maximum value of this function?
8
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use the graph of the function to estimate the intervals on which the fu…
Increasing: $(-2.5, 1)$ Decreasing: $(-\infty, -2.5) \cup (1, \infty)$
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look at this graph: what is the minimum value of this function?
$-4$
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look at this graph: what is the maximum value of this function?
4
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question a quadratic function $f(x)$ is hidden from view. you must find…
The vertex form of a quadratic function, written as $f(x)=a(x-h)^2+k$ where $(h,k)$ is the vertex. The minimum value of the function is $k$, which is directly visible in this form.
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look at this graph: what is the minimum value of this function?
0
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question simplify the expression below using order of operations. $1 + …
7
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a plane crosses the atlantic ocean (3000 miles) with an airspeed of 500…
(a) Cost at 360 mph: $\$295.00$; Cost at 490 mph: $\$284.72$ (b) Domain: All positive real numbers, or $x>0$ (d) | x | C(x) | |-----|---------| | 450 | $\$286.25$ | | 500 | $\$284…
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look at this graph: what is the maximum value of this function?
6
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look at this graph: what is the minimum value of this function?
-10
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look at this graph: what is the maximum value of this function?
5
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graph this function. $y = \\frac{5}{6}(3)^x$ plot two points to graph t…
Plot the points $(0, \frac{5}{6})$ (or $(0, 0.83)$) and $(1, 2.5)$ on the coordinate grid, then draw a smooth exponential curve passing through them.
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function a function b $y = 2x + 2$ which statement is true? the slope o…
The slope of Function A is less than the slope of Function B.
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look at this graph: what is the maximum value of this function?
6
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look at this graph: what is the maximum value of this function?
5
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write the function shown in the graph to the right. write the function …
$\boldsymbol{y=\sqrt{x+4}}$
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given the piecewise defined function:$f(x)=\begin{cases}-2x - 5 & \text…
- For $x\leq-3$: A line passing through $(-3, 1)$ (closed dot) and $(-4, 3)$, extending leftward. - For $x>-3$: A line passing through $(-3, 2)$ (open dot) and $(0, 5)$, extending…
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finding the domain and range of a graph determine the domain and range …
Domain: $[-4, 0]$ Range: $[-5, 5]$
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in the problem, $f(x)=\\log_{2}x$ and $g(x)=\\log_{10}x$. for $x>1$, th…
f
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given the function $f(x)=\\begin{cases}8x - 5&x < 0\\\\\\sqrt{8x^2 + 25…
$f(-1) = -13$ $f(0) = 5$ $f(2) = 7.550$
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in the problem, $f(x) = \\log_{2}x$ and $g(x) = \\log_{10}x$. for $x > …
The graph of $f(x)=\log_2 x$ increases faster for $x>1$.
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given the function $n(x) = \\begin{cases} x - 9 & x < -5 \\\\ 5x^2 - 2x…
$n(-1)=5$ $n(7)=33$ $n(-9)=-18$ $n(-5)=133$ $n(1)=1$ $n(-10)=-19$
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in the problem, $f(x)=\\log_{2}x$ and $g(x)=\\log_{10}x$. which point d…
$(1, 0)$
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in the problem, $f(x)=\\log_2 x$ and $g(x)=\\log_{10} x$. how are the g…
A. Both increase from left to right. B. Both have an asymptote of $x = 0$.
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2. in the following exercises, convert the mixed number to an improper …
a) $\frac{5}{3}$ b) $\frac{7}{5}$ c) $\frac{9}{4}$ d) $\frac{17}{6}$ e) $\frac{25}{9}$ f) $\frac{19}{7}$ g) $\frac{25}{7}$ h) $\frac{32}{9}$ i) $\frac{43}{8}$
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why are the books burned? according to beatty, why do the firemen burn …
To limit discussion, disagreement and conflict in society.
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what happens to the value of $f(x) = \\log_{4} x$ as $x$ approaches 0 f…
1. As $x$ approaches 0 from the right, the value of $f(x)=\log_4 x$ approaches $-\infty$ (decreases without bound). 2. As $x$ approaches $+\infty$, the value of $f(x)=\log_4 x$ ap…
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the x-intercept of $f(x) = \\log_{4} x$ is
$1$
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which of the following explains why $f(x)=\\log_{4}x$ does not have a $…
1. Its inverse does not have any x-intercepts. 2. There is no power of 4 that is equal to 0.
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which graph shows the logarithmic function $f(x)=\\log_{0.5}x$?
The top graph (the first one shown) represents the function $f(x)=\log_{0.5}x$.
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$x - y = 9$ $y = x + 9$
The inequality $-9 < 9$ is always true, meaning all values of $x$ and $y$ that satisfy $y = x - 9$ will also satisfy $y < x + 9$. The solution set is all pairs $(x, x-9)$ where $x…
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the point $(-1, 0.5)$ lies on the graph of $f^{-1}(x)=2^{x}$. based on …
(0.5, -1)
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what is the inverse of the logarithmic function $f(x)=\\log_{2}x$? $f^{…
$\boldsymbol{f^{-1}(x) = 2^x}$
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9. what is the slope of the line shown in the graph, given that point a…
2
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a plane crosses the atlantic ocean (3000 miles) with an airspeed of 500…
(a) Cost at 360 mph: $\$295.00$; Cost at 490 mph: $\$284.72$ (b) Domain: All positive real numbers, $x>0$ (c) Correct graph: A (d) | x | C(x) | |-----|------------| | 450 | $\$286…
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consider $f(x)=b^x$. which statement(s) are true for $0 < b < 1$? choos…
- The range is $y > 0$. - The graph has a y-intercept of 1. - The domain is all real numbers. - The function is always decreasing.
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let a and b be real numbers where a ≠ b ≠ 0. which of the following fun…
$f(x) = x(x - a)^2(x - b)^4$
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which graph has the same end behavior as the graph of $f(x)=-3x^4 - x^2…
The bottom graph (the one where both ends of the curve point downward towards negative infinity) has the same end behavior as $f(x) = -3x^4 - x^2 + 1$.
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date: feb 6, 2026period: 3average rate of change (given a function) maz…
The correct maze path and calculations are: 1. START box: Average rate of change = $9$ 2. $f(x)=x^2+8x+18$, $[-7,-3]$: Average rate of change = $-2$ 3. $f(x)=\frac{1}{2}x^2+2x-1$,…
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which statement describes the graph of $f(x) = 4x^7 + 40x^6 + 100x^5$?○…
The graph crosses the x-axis at x = 0 and touches the x-axis at x = -5.
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what is the end behavior of the graph of the polynomial function $f(x) …
D. As $x \to -\infty, y \to \infty$ and as $x \to \infty, y \to \infty$.
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a polynomial function has a root of $-4$ with multiplicity 4, a root of…
The bottom graph (the lower of the two provided graphs, with end behavior falling to the left and rising sharply to the right, showing a touch at an x-intercept, a flattened cross…
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1) $y > \\frac{1}{3}x + 1$ $y < \\frac{4}{3}x - 2$ 12) $y \\geq \\frac{…
The solution is the overlapping shaded area above $y=\frac{1}{3}x+1$ (dashed) and below $y=\frac{4}{3}x-2$ (dashed). --- ### For Problem 12: $y\geq\frac{5}{2}x-3$, $y\leq-\frac{1}…
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1. which is the product? use an area model to solve. $\frac{2}{7} \time…
B. $\frac{4}{3}$
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which is the graph of $f(x) = 4^x$?
The graph on the left (the exponential curve passing through (0,1), increasing upwards on the right, and approaching the x-axis on the left) is the graph of $f(x)=4^x$.
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use descartes rule of signs to find how many possible negative real roo…
0
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use descartes rule of signs to find how many possible positive real roo…
4, 2 or 0
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question 19 of 20 which line of dialogue best provides insight about a …
D. "Don't call me a 'millennial,'" I spat out the word. "I'm not like my peers, who post every sneeze on social media, thinking the sun rises and sets on them."
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use descartes rule of signs to find how many possible positive real roo…
4, 2 or 0
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use descartes rule of signs to find how many possible negative real roo…
1
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use descartes rule of signs to find how many possible positive real roo…
3 or 1
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use descartes rule of signs to find how many possible negative real roo…
2 or 0
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the equation of the piecewise defined function $f(x)$ is shown. what is…
$f(1) = -1$
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analyzing word choice: figurative language — instruction — level h brig…
realize the value
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$20+20+6-40$
6
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determine whether the function represents exponential growth or decay. …
The function $y = 100 \cdot 3.1^x$ represents exponential **growth**. Rewriting the base in terms of the rate of growth or decay results in the function $y = 100 \cdot (1+2.1)^x$.…
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write a function g(x) that represents the exponential function $f(x)=3^…
$g(x) = -4\cdot 3^x$ ### Graphing Notes (for context): - For $f(x)=3^x$: This is a standard exponential growth function, passing through $(0,1)$, increasing as $x$ increases, appr…
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part 1 of 2 identify the transformation from the parent function $f(x)=…
The graph of f(x) is **reflected and stretched** vertically **by a factor of 6**, and **shifted left 4** unit(s).
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20. the volume of a cylindrical tin can with a top and a bottom is to b…
D. 4
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q12 integration with completing the square an antiderivative for $\frac…
$\arctan(x-1) + C$ (where $C$ is the constant of integration)
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question 4 of 6 cason wants to diversify his investment portfolio. caso…
B. Hire a Financial Advisor
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the number of positive real roots it has is equal to the number of sign…
2 or 0
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graph $y = 2x - 6$.
The graph is a straight line passing through points $(0, -6)$ and $(1, -4)$, with a slope of 2 and y-intercept at $(0, -6)$.
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the points in the table lie on a line. find the slope of the line. x: 0…
1
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the points in this table lie on a line. find the slope of this line x 0…
1
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passed as a result of franklin delano roosevelts presidencies, what did…
1. Limited the number of times a person can be elected president to 2 times 2. U.S. Senators
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given the equation: $f(x) = 4^{x+2}+2$, answer the following: a. growth…
A. growth B. $-2$ C. $2$ D. $y=2$ E. $(-1, 6)$
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| $x$ | 0 | 1 | 2 | 3 || ---- | ---- | ---- | ---- | ---- || $f(x)$ | 5…
E. 13
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what is the solution to the equation $2^{5x}=6$? enter the answer to th…
0.52
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what is happening to this graph when the x-values are between -8 and -4…
A. It is decreasing.
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identify the range of the function shown in the graph. a. y is all real…
B. $y>0$
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this is the graph of the equation $y = \\frac{6}{5}x$. which ordered pa…
(-5, -6)
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a student wants to graph the exponential function $f(x)=3(2)^x$. which …
The function has a y-intercept at (0, 3) and contains the points (1, 6), (2, 12), and (3, 24).
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$int 6sin(pi+x)sin(2pi-x)dx$
$3x - \frac{3}{2}\sin2x + C$
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graph the following function on the given coordinate plane and identify…
# Explanation (First Function: $f(x)=\frac{x^2-3x-10}{x^2-4}$): ## Step1: Factor numerator and denominator Numerator: $x^2-3x-10=(x-5)(x+2)$ Denominator: $x^2-4=(x-2)(x+2)$ Simpli…
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3 fill in the blank 1 point $f(x)=3x+5$ $f(-2)=$ 4 fill in the blank 1 …
1. $f(-2)=-1$ 2. $f(4)=1$ 3. No input value provided to evaluate $f(x)=-4x+10$; the function is $f(x)=-4x+10$
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read the paragraph. to conserve fuel and save lives, the national speed…
persuade drivers to slow down
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question 2 (10 points) by the end of the month, maria spent more than s…
- Sign up for overdraft protection with her bank. - Monitor her spending and maintain a positive balance. --- # Question 3
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$y = -\frac{4}{3}x - 2$ select points on the graph to plot them.
Los puntos a graficar son $(0, -2)$, $(3, -6)$ y $(-3, 2)$; al unirlos se obtiene la recta de la ecuación $y = -\frac{4}{3}x - 2$.
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which graph shows an exponential function that nears a constant value a…
A. W