Calculus
Limits, derivatives, optimization, and behavior of functions.
-
use the graph of g(x) to complete the table. x | g(x) -9 | -8 | -4 | 2
| $x$ | $g(x)$ | |-----|--------| | -9 | 8 | | -8 | 5 | | -4 | 2 |
-
use the graph of ( f(x) ) to complete the table. the table has columns …
For $x=-7$, $f(x)=0$ For $x=5$, $f(x)=-3$ Completed table: | $x$ | $f(x)$ | |-----|--------| | -10 | -2 | | -7 | 0 | | 5 | -3 |
-
pizza general charges 10 dollars per medium pizza. fill in the vertical…
10
-
pair compare! 20 8 + 14
$20 < 8 + 14$ (select the $<$ symbol)
-
pair compare! -4 + 15 11
$=$
-
document f source: adapted from colin mcewan, the first world war: euro…
12,740,000 square miles ### Question 2
-
pair compare! 0 4 + 15 19 next →
$4 + 15 = 19$
-
the slope of a line passing through (2, 6) and (5, 12) is: a. 2 b. 3 c.…
a. 2 ### Second Question:
-
hing exponential functions $f(x)=2^{x - h}$, for $h>0$, will shift the …
\( f(x)=2^{x}-k \), for \( k > 0 \), will shift the graph down.
-
this is a multi - part item. consider the transformation $f(x)=2^{x - h…
The true statement is: \( \boldsymbol{f(x)=2^{x - h},\text{ for }h > 0,\text{ will shift the graph right}} \)
-
a ball is thrown from an initial height of 3 meters with an initial upw…
\( t = 0.76 \) or \( t = 1.84 \)
-
a ball is thrown from a height of 25 meters with an initial downward ve…
\(t\approx1.79\) seconds
-
15) solve the following inequalities: a) \\( \\frac{2}{3}(2 - x) > \\fr…
\(x < \frac{1}{2}\) ### 15b) Solve \(\boldsymbol{x^2 - 16<6x}\)
-
question 10 of 10 for the function $f(t)=pe^{rt}$, if $p = 7$ and $r = …
B. 11.4
-
which of the following were direct consequences of executive order 9066…
- Japanese Americans were relocated to internment camps - Civil rights of Japanese Americans were limited
-
which statement expresses the central theme of this selection? a slaver…
C. Several European countries played an integral role in the development and growth of the lucrative, yet abhorrent, transatlantic slave trade.
-
find an expression for the function whose graph is the given curve. the…
\( 6 - \sqrt{-x} \)
-
type a second equation to graph a line that will make a system of equat…
$\boldsymbol{2y = 6x + 4}$ (any non-zero scalar multiple of $y=3x+2$ is valid)
-
15. critique the reasoning of others. kyla was asked to solve the syste…
Kyla is not correct. The actual solution to the system is $(2, 1)$, as this point satisfies both equations: $2 + 1 = 3$ and $2 - 3(1) = -1$. Kyla's error is that the lines she gra…
-
find the domain of the function. (enter your answer in interval notatio…
\((-\infty,0)\cup(7,\infty)\)
-
evaluate the difference quotient for the given function. simplify your …
\( -5 - h \)
-
given the graph of $y = f(x)$, shown as a red dashed curve, drag the gr…
To draw \( y = f(-x) \), reflect the graph of \( y = f(x) \) (red dashed curve) over the \( y \)-axis. Move the "Drag Function" and "Control Width" green points to their mirror - …
-
question the graph of ( y = f(x) ) is shown as a red dashed curve with …
To draw the graph of \( y = -f(x) \), reflect each of the points A, B, C, and D over the \( x \)-axis. That is, for each point \( (x, y) \) on \( y = f(x) \), move it to \( (x, -y…
-
Question was provided via image upload.
As $x \to +\infty$, $y \to -\infty$; As $x \to -\infty$, $y \to +\infty$ (For the practical farming context where nitrogen application $x \geq 0$: As the amount of nitrogen applie…
-
which statement primarily appeals to logos to support the position that…
The statement "Although it may come as a surprise, I would prefer a year - round school schedule to our current system. As an academically competitive high school junior, I would …
-
what is the slope of this line? simplify your answer and write it as a …
2
-
what is the slope of this line? simplify your answer and write it as a …
\( 0 \)
-
what is the slope of this line? simplify your answer and write it as a …
\(-\frac{1}{5}\)
-
what is the slope of this line? simplify your answer and write it as a …
\(\frac{5}{2}\)
-
what is the slope of this line? simplify your answer and write it as a …
\(-\frac{5}{8}\)
-
4. describe the transformation of $h(x) = 2^{x + 3}$. list the followin…
a. y-intercept: $8$ b. Domain: All real numbers ($(-\infty, \infty)$) c. Range: All positive real numbers ($(0, \infty)$) d. Asymptote: $y=0$
-
what is the slope of this line? simplify your answer and write it as a …
\(-1\)
-
what is the slope of this line? simplify your answer and write it as a …
\(-\frac{3}{5}\)
-
what is the slope of this line? simplify your answer and write it as a …
\(\frac{2}{3}\)
-
what is the slope of this line? simplify your answer and write it as a …
\(1\)
-
what is the slope of this line? simplify your answer and write it as a …
\(1\)
-
what is the slope of this line? simplify your answer and write it as a …
\( 1 \)
-
what is the slope of this line? simplify your answer and write it as a …
\(-3\)
-
select the checkbox for each correct choice to fill it in. be sure to m…
A. \(1\cdot1 = 1\), B. \(1 + 1=2\), D. \(1\cdot2 = 2\)
-
5. $5\\frac{1}{4} \\div 8\\frac{1}{2}$ 6. $\\frac{8}{16} \\div \\frac{1…
5. $\frac{21}{34}$ 6. $\frac{1}{4}$ 7. $\frac{12}{11}$ or $1\frac{1}{11}$ 8. $\frac{6}{85}$
-
which inequality is less than the quadratic function with zeros (-7) an…
B. $y<\frac{3}{2}x^2 + 9x - \frac{21}{2}$
-
evaluate. do not round your answer.\\(0.93^{3}\\)
$0.804357$
-
forms of government: latin america the government of each country can b…
| Facts | Type of Government | Head of Government is elected by... | Terms of Office | Voting Age | |-------|--------------------|-------------------------------------|-----------…
-
the graph of $y = f(x)$ is graphed below. what is the end behavior of $…
As \( x \to -\infty \), \( f(x) \to -\infty \); as \( x \to +\infty \), \( f(x) \to +\infty \)
-
solve the following system of equations graphically on the set of axes …
The solution to the system is $\boldsymbol{(6, 6)}$ (this is the point where the two lines intersect on the graph)
-
evaluating functions the graph of the function ( k(x) ) is shown below.…
$k(2)=4$ $x=-3$
-
select all that apply which of the following are nontariff barriers? (m…
A. Lengthy customs procedures B. Import licensing restrictions C. Limits on the quantity of a product that may be imported D. Product testing requirements
-
background information: in the immediate aftermath, survivors searched …
A. The city had turned into an unfamiliar wasteland, and many people were gone.
-
to make 77 + 48 easier to solve, lou decides to first add on from 77 to…
125
-
49 to make 77 + 48 easier to solve, lou decides to first add on from 77…
3
-
to make $48 + 34$ easier to solve, lou decides to first add on from 48 …
82
-
to make 48 + 34 easier to solve, lou decides to first add on from 48 to…
$2$
-
fractions - add, subtract, multiply, and divide 1 $\frac{17}{3} + \frac…
$\frac{298}{51}$ (or $5\frac{43}{51}$) ### Problem 2: $\boldsymbol{\frac{7}{2} + \frac{11}{13}}$
-
multiplying mixed numbers change mixed numbers into improper fractions …
\( 12\frac{3}{5} \) Let's solve problem 3: \( 4\frac{1}{3} \times 1\frac{7}{8} \)
-
lou wants to make 96 + 56 easier to solve in his head. he decides to ad…
152
-
multiply these fractions. cancel and simplify if necessary. 1. $1\\frac…
\( 2\frac{5}{8} \) ### Problem 2: \( 2\frac{1}{3} \times 5\frac{2}{5} \)
-
select the correct answer. what is the solution to this equation? \\(\\…
B. $x = -1$
-
math 30 pre - calculus section 9.2 bw 1: find the x and y intercepts, t…
- x - intercept: None. - y - intercept: \( (0,-\frac{1}{8}) \). - Vertical asymptotes (points of discontinuity): \( x=-4 \), \( x = 2 \). - Horizontal asymptote: \( y = 0 \). - Si…
-
graph the equation ( y = x - 1 ). let ( x = -3, -2, -1, 0, 1, 2 ), and …
-4
-
1. what limits the amount of money a pac can contribute to a candidate?…
Federal election law regulations
-
introduction: match each word with the correct definition. convey kamik…
Convey → to communicate, or make an impression Kamikaze → Japanese pilots who attempted suicide missions into enemy planes Strongholds → secure places Embargo → official governmen…
-
introduction: match each word with the correct definition. convey kamik…
Convey — to communicate, or make an impression Kamikaze — Japanese pilots who attempted suicide missions into enemy planes Strongholds — secure places Embargo — official governmen…
-
what is the slope of this line? simplify your answer and write it as a …
$\frac{2}{3}$
-
question the polynomial function $f(x)$ is graphed below. fill in the f…
- The degree of \( f(x) \) is \( 4 \) (cuatro) and the leading coefficient is negative. There are \( 3 \) different real zeros and \( 3 \) relative extremes. Wait, pero la gráfica…
-
find the inverse function in slope - intercept form (mx + b): $f(x)=\fr…
\( f^{-1}(x) = \frac{3}{5}x + 9 \)
-
example 3: graph the function $-2\\sqrt3{x + 5}$ and identify the domai…
- **Domain**: \( (-\infty,\infty) \) - **Range**: \( (-\infty,\infty) \) - **Graph**: A smooth curve (cubic - like) shifted 5 units left, stretched vertically by a factor of 2, an…
-
directions: match the expressions and domain intervals for the given pi…
To solve this, we analyze the piecewise graph by identifying the slope and y - intercept of each segment and matching it with the given expressions and domain intervals. ### Step …
-
cket: intro to civil rights scenario: during wwii, black and white sold…
The violation of the 14th Amendment is: Black soldiers had inferior supplies and lack of opportunities The government action that addressed this situation is: Executive Order 9981
-
cket: intro to civil rights scenario: during wwii, black and white sold…
Black soldiers had inferior supplies and lack of opportunities
-
with others if they so choose. faye recommends that creating a code of …
Links to resources about technological use time limits and mental health The expectation that all are welcome, regardless of differences Instructions on how to communicate with on…
-
solve for x \\begin{cases} y \\geq 2x - 1 y < -x + 4 \\end{cases}
$x < \frac{5}{3}$
-
which number is closest to $-sqrt{212}$? -14.2 -14.5 -14.8 -13.9
-14.5
-
which number is closest to \\(\\sqrt{108}\\) ? 10.3 10.8 9.9 10.7
10.3
-
which number is closest to $-sqrt{128}$? -12.2 -10.7 -10.6 -11.3 submit
-11.3
-
which number is closest to $-sqrt{114}$? -9.5 -10.6 -11.1 -10.1 submit
-10.6
-
7. consider the polynomial function: ( f(x) = -(x + 2)(x - 1)(x - 2) ) …
End - behavior: As \( x ightarrow+\infty \), \( f(x) ightarrow-\infty \); as \( x ightarrow-\infty \), \( f(x) ightarrow+\infty \). Number of local maxima: 1. ### Question 8
-
the exponential function h, whose graph is given below, can be written …
$h(x)=3\cdot 2^x$
-
evaluating functions use the function f(x) = 3x + 9 to answer the follo…
$f(0)=9$ $x=-5$
-
select all of the following graphs which are one-to-one functions.
- The top graph (decreasing curve starting at (1,1)) - The middle graph (increasing curve starting left flat) - The bottom graph (straight line with positive slope)
-
question #7 the house of representatives is intended to reflect the pop…
C. The total number of representatives is divided or allocated by population ### Question #8
-
question #3 in the cartoon above, mr. d.c. (the man in the tri - corner…
Popular sovereignty (the option with "Popular sovereignty" text, as per the choices: the fourth option in the list shown, labeled "Popular sovereignty").
-
use a calculator to approximate the number below. $10.1^{5}$ $10.1^{5}\…
\(10.1^{5}\approx105101.0050\) (rounded to four decimal places)
-
6. which graph below has a midline of about 1, an amplitude of 5, and a…
B. The graph with midline about 1, amplitude of 5, and period of 3
-
part iii: giuseppe garibaldi — action on the ground 11. describe giusep…
Giuseppe Garibaldi was an Italian nationalist, military leader in the Risorgimento. He’s a “romantic hero” for his daring (e.g., Thousand expedition to Sicily), idealistic dedicat…
-
question 4 of 10 which of the following enlightenment ideas influenced …
C. Leaders do not have the right to oppress their people.
-
what is an artistic medium? a. an informal saying that is more appropri…
C. The means by which something is communicated, or the material something is created from
-
6. find the value of the absolute maximum and where it occurs, without …
The absolute maximum value is $1$, and it occurs at $x=1$.
-
guided practice use what you have learned about the parts of exponentia…
1. a. $y = 1.5(2)^x$ b. 96 inches 2. a. $y = 10000(2)^{\frac{x}{7}}$ b. $\approx \$46,650$
-
find the values of the absolute extrema and where they occur, without t…
Absolute minimum: $0$ at $x=1$; Absolute maximum: $8$ at $x=3$ ---
-
lets practice! 1. given the exponential function ( y = 3(5)^x ) a. stat…
1. a. 3 b. 5 c. Growing d. Starts at 3, multiplies by 5 for each increase of 1 in $x$. e. 375 2. a. 32 b. 0.25 c. Decaying d. Starts at 32, multiplies by 0.25 for each increase of…
-
derivatives of inverse functions 1) let ( f(x) = x^5 + 2x^3 + x - 1 ). …
a. $f(1)=3$, $f'(1)=12$ b. $f^{-1}(3)=1$, $(f^{-1})'(3)=\frac{1}{12}$ --- ### 2)
-
question 2 of 12 which of the following ratios correctly describes the …
C. $\frac{adj}{hyp}$
-
6. evaluate the following derivatives on your calculator. be sure to in…
(a) $1$ (b) The derivative does not exist at $x=3$ (right-hand derivative is $\frac{1}{2}$) (c) $\approx 0.275$ (exact value: $\frac{1}{2\sqrt{3.3}}$)
-
question 7 of 10 what is \\(\\tan 60^{\\circ}\\)? a. 1 b. \\(\\frac{1}{…
F. $\sqrt{3}$
-
7 use your calculator to sketch the graph of the derivative of the foll…
(a) $g'(x)=\cos x$ (b) $f'(x)=\frac{1}{x}$ (for $x>0$) (c) $y'=\tan x$ (for $x eq \frac{\pi}{2}+k\pi, k\in\mathbb{Z}$) --- ### For Question 8:
-
1) $f(x)=x^3 + x - 1$ on $0,1$ 2) $f(x)=\\begin{cases}x - 5, & x\\leq 2…
The function is continuous on $[0,1]$. $f(0)=-1$, $f(1)=1$, so IVT applies: for any value between $-1$ and $1$, there exists a $c \in (0,1)$ where $f(c)$ equals that value. --- ##…
-
for each of problems 1-5, determine whether or not the intermediate val…
The Intermediate Value Theorem applies. $f(x)$ is continuous on $[0,1]$, $f(0)=-1<0$, and $f(1)=1>0$, so there is a zero in $(0,1)$. --- ### Problem 2
-
find the correct sum. write your answer as a mixed number. \\(\frac{5}{…
The sum is $3\frac{3}{6}$ (or simplified to $3\frac{1}{2}$, but based on the denominator 6, it's $3\frac{3}{6}$). So the whole number is 3, numerator is 3, denominator is 6.
-
find the sum. write your answer as a mixed number. \\( 4\\frac{5}{8} + …
$5\frac{1}{2}$
-
choose the sum that is greater than 5. $4\\frac{1}{8}+\\frac{5}{8}$ $4\…
\(4\frac{5}{8}+\frac{7}{8}\)