微積分
極限、導數、最優化與函數性質。
-
compare ( g(x) = -1.5x^2 - 4.5x + 10 ) to ( f ), shown in the graph. wh…
C. f(x); The y-coordinate of the vertex of f(x) is greater than the y-coordinate of the vertex of g(x).
-
3. what was life like in a trench? a. trenches were the safest place to…
B. Trenches were extremely dangerous and uncomfortable ### Question 4
-
y = -(x - 1)^3
The graph shown does not match the function \( y = -(x - 1)^3 \). The correct key points for \( y = -(x - 1)^3 \) are: when \( x = 1 \), \( y = 0 \); \( x = 2 \), \( y=-1 \); \( x…
-
find the y-intercept, the axis of symmetry, and the vertex of the graph…
- The y - intercept is \( (0, - 3) \) - The axis of symmetry is \( x=-1 \) - The vertex is \( (-1, - 2) \)
-
the trajectory of the water from fountain a is represented by a functio…
Fountain A has a vertex of $(1, 8)$ while Fountain B has a vertex of $(-4, 6)$, so the water from Fountain A reaches a greater height.
-
details no additional details were added for this assignment. assignmen…
$x = \frac{13}{12}$
-
what is the y - intercept of the function? $f(x)= - 0.2x^{2}+0.3x - 0.8…
\((0, - 0.8)\)
-
tyler is building a pen for his rabbit on the side of the garage. he ne…
### Part 1: Completing the Area Table To find the area of a rectangle, we use the formula \( \text{Area} = \text{length} \times \text{width} \). Let's calculate the area for each …
-
10. $f(x)=\\begin{cases}2x + 5 & \\text{if } x < -4 \\\\ x^2 + 3x & \\t…
(for \( x = -5 \)): \(-5\)
-
sketch the graph of the quadratic function and the axis of symmetry. $f…
The axis of symmetry is the vertical line \( x = -2 \). The graph of \( f(x) = -3(x + 2)^2 + 4 \) is a parabola opening downward with vertex at \((-2, 4)\), and the axis of symmet…
-
12 identify where the function is increasing and where it is decreasing…
d) increasing \( -1 < x < \infty \) and decreasing \( -\infty < x < -1 \) ### Problem 13
-
find the slope of the line that passes through (5, 8) and (3, 13). simp…
$-\frac{5}{2}$
-
find the slope of the line that passes through (6, 3) and (3, 1). simpl…
$\frac{2}{3}$
-
identify the vertex, axis of symmetry, and direction of the graph of ea…
\((1, -6)\)
-
find the slope of the line that passes through (10, 6) and (3, 7). simp…
$-\frac{1}{7}$
-
how do the average rates of change for the pair of functions compare ov…
The average rate of change of \( f(x) \) over \( 1\leq x\leq6 \) is \( 0.7 \). The average rate of change of \( g(x) \) over \( 1\leq x\leq6 \) is \( 2.8 \). The average rate of c…
-
over what interval is the function increasing, and over what interval i…
The function \( f(x) \) is decreasing over the interval \( x < 0 \).
-
over what interval is the function increasing, and over what interval i…
The function \( f(x) \) is increasing over the interval \( x \geq 0 \) and decreasing over the interval \( x \leq 0 \).
-
find the slope of the line that passes through (10, 10) and (1, 5). sim…
$\frac{5}{9}$
-
how does the value of a in the function affect its graph when compared …
B. The graph of \( h(x) \) is wider, C. The graph of \( h(x) \) opens upward
-
why was the first draft of the articles of confederation revised? it pr…
It proposed a strong central government.
-
how does the value of a in the function affect its graph when compared …
A. The graph of \( h(x) \) is wider C. The graph of \( h(x) \) opens downward
-
how does the value of a in the function affect its graph when compared …
A. The graph of \( g(x) \) is narrower, D. The graph of \( g(x) \) opens upward
-
graph this line using the slope and y - intercept: ( y = \frac{1}{8}x +…
Plot the points $(0, 5)$ and $(2, 6)$, then draw a straight line passing through these points to represent the line $y=\frac{1}{2}x+5$.
-
a computer game designer uses the function $f(x)=4(x - 2)^2 + 6$ to mod…
\((-1,42)\)
-
question #2 - 20 points the zeros of a polynomial function are: -2, 0, …
1. $P(x) = ax(x+2)(x-1)(x-3)$ (or the simplest form $P(x)=x(x+2)(x-1)(x-3)$ when $a=1$) 2. 4 3. As $x\to+\infty$, $P(x)\to+\infty$; as $x\to-\infty$, $P(x)\to+\infty$ 4. $(0, 0)$ …
-
write an explicit formula for $a_n$, the $n^{\text{th}}$ term of the se…
\(a_{n}=23 - 8n\)
-
the graph represents a quadratic function. write the function in vertex…
\(f(x) = (x + 3)^2 - 8\) (assuming \(a = 1\), or with the correct \(a\) found, but since the problem says "Do not simplify", and the vertex is \((-3, -8)\), the vertex form is \(f…
-
the height of a diver above the water, is given by $h(t) = -5t^2 + 10t …
B. The diver begins 3 meters above the water. C. The function has 1 zero that makes sense in this situation.
-
sketch the graph of the quadratic function and the axis of symmetry. $f…
The axis of symmetry is \( x = -4 \). To sketch the graph: plot the vertex \((-4, 2)\), draw the parabola opening downward (using symmetric points) as a solid curve, and draw the …
-
sketch the graph of the function. $f(x)=0.5(x + 4)^2 + 2$ use the graph…
The graph of \( f(x)=0.5(x + 4)^2 + 2 \) is a parabola with vertex at \((-4, 2)\), opening upward, and axis of symmetry \( x=-4 \). To sketch it, plot the vertex, use the directio…
-
details no additional details were added for this assignment. assignmen…
$0$
-
sketch the graph of the quadratic function and the axis of symmetry. $f…
The axis of symmetry is the vertical line \( x = -2 \), and the graph of the quadratic function \( f(x) = -3(x + 2)^2 + 1 \) is a parabola opening downward with vertex at \( (-2, …
-
identify the vertex, axis of symmetry, and direction of the graph of ea…
\((-1, -1)\)
-
identify the vertex, axis of symmetry, and direction of the graph of ea…
B. The graph is wider than \( f(x)=x^2 \)
-
part 4 of 4 identify the vertex, axis of symmetry, and direction of the…
A. The graph has the same width as \( f(x)=x^2 \)
-
f(x) = x^2 - 2; -2, -1 use the given function or the graph to find the …
\(-3\)
-
consider the graph. what is the average of change on the interval ( 2 l…
5
-
the graph shown is a translation of the graph of $f(x)=x^2$. write the …
\( f(x)=(x - 3)^2 + 4 \)
-
use the graph to determine the following a. the functions domain b. the…
a. $[0, 4]$ b. $[-9, 7]$ c. A. The x-intercept(s) is(are) $3$ d. The y-intercept is $-9$ e. $f(1) = -5$
-
consider the graph. what is the average of change on the interval ( 2 l…
5
-
identify the vertex and the axis of symmetry for the function.\\( f(x)=…
\((0, 5)\)
-
question 7 (1 point) the zero lower bound for interest rates implies an…
D. The exchange rate (E) equals \( E^e / (1 - R^* ) \), where \( R = 0 \), creating an upper bound \( E^{\text{max}} \), while the liquidity trap results in a horizontal money dem…
-
the graph shown is a translation of the graph of $f(x)=2x^2$. write the…
\( f(x) = 2(x - 1)^2 - 2 \)
-
details no additional details were added for this assignment. assignmen…
The exact solution (using exponents) is $x = \frac{e^4 - 4}{6}$ The solution, rounded to 4 decimal places is $x = 8.4330$
-
five limits on government constitution: a constitution is ______ limits…
To solve this fill - in - the - blank problem about the five limits on government, we analyze each section based on the knowledge of political science (a subfield of Social Scienc…
-
the graph of a piecewise - defined function is given. write a definitio…
\(f(x)=\begin{cases}-\frac{1}{4}x & \text{if } - 8\leq x\leq0\\-x & \text{if } 0\lt x\leq3\end{cases}\)
-
the graph of a piecewise - defined function is given. write a definitio…
The piecewise function is \( f(x)=\begin{cases}-x&\text{if }-3\leq x\leq0\\1&\text{if }0\lt x\leq3\end{cases} \) (Note: There might be a discrepancy between the graph and the give…
-
a burrito company uses the function $c(x) = 1.74x^2$ to calculate the n…
Between 6 and 8 inches, the calories in a tortilla \(\boldsymbol{\text{increase}}\) by about \(\boldsymbol{24.36}\) calories per inch, and between 9 and 11 inches, the calories in…
-
a burrito company uses the function $c(x) = 1.74x^2$ to calculate the n…
34.8
-
a burrito company uses the function $c(x)=1.74x^2$ to calculate the num…
24.36
-
how do the average rates of change for the pair of functions compare ov…
The average rate of change of \( f(x) \) over \( - 6\leq x\leq - 3 \) is \( 63 \). The average rate of change of \( g(x) \) over \( - 6\leq x\leq - 3 \) is \( 189 \). The average …
-
how do the average rates of change for the pair of functions compare ov…
The average rate of change of \( f(x) \) over \( 1\leq x\leq6 \) is \( 5.6 \). The average rate of change of \( g(x) \) over \( 1\leq x\leq6 \) is \( 16.8 \). The average rate of …
-
what is the quotient when the decimal number ten and six tenths is divi…
265
-
over what interval is the function increasing, and over what interval i…
# Explanation: ## Step1: Analyze the function values We have the function \( f(x) = 8x^2 \) (wait, actually looking at the table, when \( x=-2 \), \( f(x)=32 \); \( x = - 1 \), \(…
-
over what interval is the function increasing, and over what interval i…
\( x < 0 \) (or in interval notation, \( (-\infty, 0) \), but since the question asks for an inequality, \( x < 0 \))
-
over what interval is the function increasing, and over what interval i…
The function \( f(x) \) is decreasing over the interval \( \boldsymbol{x < 0} \)
-
over what interval is the function increasing, and over what interval i…
\( x > 0 \)
-
how does the value of a in the function affect its graph when compared …
C. The graph of \( h(x) \) is wider, D. The graph of \( h(x) \) opens downward
-
how does the value of a in the function affect its graph when compared …
B. The graph of \( h(x) \) is wider C. The graph of \( h(x) \) opens downward
-
how does the value of a in the function affect its graph when compared …
B. The graph of \( g(x) \) is narrower, C. The graph of \( g(x) \) opens upward
-
how does the value of a in the function affect its graph when compared …
A. The graph of \( f(x) \) is wider.
-
1 mark for review in the case wickard v. filburn (1942), roscoe filburn…
C. The expansive interpretation of the commerce clause by the Supreme Court which greatly extended the power of Congress drew criticism that eventually led to a narrower interpret…
-
how does the value of a in the function affect its graph when compared …
A. The graph of \( g(x) \) is narrower
-
tell whether each statement about a function of the form $f(x)=ax^2$ is…
always true
-
use the table to describe the intervals over which ( f(x) = 15x^2 ) is …
\( x < 0 \)
-
describe and correct the error a student made in finding the average ra…
First, the student used incorrect \( y \)-values (points \((-4, -8)\) and \((-2, -2)\) are wrong; correct points are \((-4, 8)\) and \((-2, 2)\)). Then, using the correct points, …
-
describe and correct the error a student made in finding the average ra…
C. The points used to find the slope were incorrect. The correct points are \((-4, 8)\), \((-2, 2)\) The correct slope (average rate of change) is \(-3\) (if calculating the slope…
-
consider the graph. what is the average of change on the interval ( 2 l…
7
-
the graph of the parent quadratic function $f(x)=x^2$ and that of a sec…
A. \( a < - 1 \)
-
the position of a ball after it is kicked can be determined by using th…
The maximum height the ball reaches is \( 12 \) foot(feet).
-
example3 given the graph of a function ( f ) below, approximate the max…
To solve for the maximum and minimum values of \( f \) on each interval, we analyze the graph: ### Part a: Interval \([1, 2]\) - **Step 1: Analyze the graph on \([1, 2]\)** The fu…
-
write the function in standard form. $f(x) = -5(x - 7)^2 + 13$ $f(x) = …
\(f(x)=-5x^2 + 70x-232\)
-
write the function in standard form. $f(x) = 5(x + 3)^2 - 1$ $f(x) = \\…
\(f(x)=5x^{2}+30x + 44\)
-
compare $g(x) = -3x^2 - 6x + 6$ to $f$, shown in the graph. which funct…
B. \( g(x) \); The y - coordinate of the vertex of \( g(x) \) is greater than the y - coordinate of the vertex of \( f(x) \).
-
compare $g(x)=3x^{2}+18x + 7$ to $f$, shown in the table. which functio…
A. \( g(x) \); The \( y \)-coordinate of the vertex of \( g(x) \) is less than the \( y \)-coordinate of the vertex of \( f(x) \).
-
find the y-intercept, the axis of symmetry, and the vertex of the graph…
\((0, 11)\)
-
solve for k. 2.6 = 0.71 + k k =
$1.89$
-
find the y-intercept, the axis of symmetry, and the vertex of the graph…
\( x = -4 \)
-
what is the y-intercept of the function? $f(x)=3x^{2}+4x + 5$ the y-int…
\((0, 5)\)
-
16. ( f(x) = -x^2 - 3x + 4 ) (-3, 2) extrem a and average rates of chan…
-2
-
what is the y-intercept of the function? $f(x) = -0.2x^2 + 0.5x - 0.9$ …
\((0, - 0.9)\)
-
across 1. national population count done every ten years 2. philosopher…
1. CENSUS 2. LOCKE 5. ENUMERATED 7. BIDEN 10. CHECKS 13. NEW JERSEY 16. FEDERALISM 18. FOUR 20. PHILADELPHIA 21. LAW 25. TWO 26. EIGHTY-FIVE 27. FRANKLIN 29. MADISON 31. OVERRIDE …
-
extrema and average rates of change assignment 16. ( f(x) = -x^2 - 3x +…
55 miles per hour
-
what is the y-intercept of the function?\\( f(x) = 3x^2 - 2x - 7 \\)\ t…
\((0, -7)\)
-
here is a system of equations. \\begin{cases} y = -3x - 2 \\\\ y = -x -…
The solution is the point $(1, -5)$ *(For graphing: 1. For $y=-3x-2$: plot the y-intercept $(0, -2)$, then use slope $-3$ to plot another point (e.g., $(1, -5)$) and draw the line…
-
points (2, -1), (-2,7), (1, -2), (0, -1), and (4,7) lie on the graph of…
\(x\geq1\)
-
select all the intervals where g is increasing. choose all answers that…
A. $-4 < x < -3$, C. $0.5 < x < 1.5$
-
(13) choose the correct answer. who is yente and what is her purpose? y…
13) Yente is a matchmaker who looks for husbands for her customer's daughters. 14) A dowry is a financial gift that a bride gives to her husband upon marriage. Since Tevye's famil…
-
isabel has 28 ounces of almonds to divide equally into 4 bags. in the l…
C. 18
-
given the function, answer the following questions below.\\( f(x) = -(x…
The solutions for \( x \) are \( 1 \) and \( 9 \), so \( x = 1,9 \)
-
given the function, answer the following questions.\\( f(x) = -(x - 5)^…
The solutions for \(x\) are \(x = 1\) and \(x=9\). The coordinate points of the x - intercepts are \((1,0)\) and \((9,0)\).
-
given the function, answer the following questions below.\\( f(x) = 31(…
The solutions for \( x \) are \( x = 3 \) and \( x = 7 \). The coordinate points of the x - intercepts are \( (3,0) \) and \( (7,0) \)
-
why were the land and climate of the american west challenges to westwa…
C. Conditions were harsh, and many settlers died due to lack of resources or weather ### Second Question (How did slavery pose a challenge to westward expansion?)
-
why was american indian removal considered a challenge to westward expa…
B. White citizens often and violently clashed with American Indians over natural resources and land D. White citizens consistently wanted the land American Indians occupied ### Qu…
-
multiply the fractions. express your answer in its simplest form (a) $\…
\(\frac{2}{15}\) ### Part (b)
-
attempt 1: 10 attempts remaining. the revenue, in dollars, made by an a…
The revenue per customer is changing at approximately \(\boxed{54.8}\) dollars per customer per day on the 8th day.
-
attempt 2: 9 attempts remaining. if $f(x) = \\frac{\\sqrt{x} - 7}{\\sqr…
\( f'(x)=\frac{7}{\sqrt{x}(\sqrt{x}+7)^{2}} \) and \( f'(6)=\frac{7}{\sqrt{6}(\sqrt{6}+7)^{2}}\approx\frac{385\sqrt{6}-588}{11094}\approx0.032 \) (exact form: \( \frac{7\sqrt{6}}{…
-
the total time in minutes that the operators at a call center are on th…
\( 0.61 \) minutes per customer per day
-
attempt 1: 10 attempts remaining. find $g(t)$ given $g(t) = \\frac{19e^…
\( \frac{19e^t(t^3 - 3t^2 - 5)}{(t^3 - 5)^2} \)