Calculus
Limits, derivatives, optimization, and behavior of functions.
-
the cost of manufacturing $x$ toasters in one day is given by $c(x) = -…
(a) $x=200$ (b) $(0, 200)$ (c) $(200, 400)$ (d) $x=200$ (e) 'NONE'
-
what is the domain of the function shown in the graph below?
$-6 \leq x \leq 1$ (or in interval notation: $[-6, 1]$)
-
the revenue from selling $q$ items is $r(q) = 575q - q^2$, and the tota…
Profit $P(q) = -q^2 + 564q - 125$ Derivative $P'(q) = -2q + 564$ Quantity maximizing profit $q = 282$
-
suppose $c(x) = 0.02x^2 + 2x + 3800$ is the total cost of a company to …
$A'(x) = 0.02 - \frac{3800}{x^2}$ $x = 435.89$ units
-
a supply company manufactures copy machines. the unit cost c (the cost …
19465
-
suppose the position of a particle, $s(t)$ is given by $s(t)=t^{2}-4t+3…
(a) $v(t)=2t-4$ (b) 2 feet per second (c) $t=2$ seconds
-
evaluate. $0.07^2$
0.0049
-
evaluate. $0.03^2$
0.0009
-
graph these equations:$y = -x - 3$$y = -x - 3$click to select points on…
The line passes through points $(0, -3)$, $(1, -4)$, $(-1, -2)$ and extends infinitely in both directions on the coordinate plane.
-
$f(x) = -4x^3 + 18x^2 + 48x + 6$ is increasing on the interval ( $squar…
Increasing interval: $(-1, 4)$ Decreasing intervals: $(-\infty, -1)$ and $(4, \infty)$ Relative maximum at $x=4$
-
write an equation for the quadratic function $f$ whose graph passes thr…
$f(x) = -3x^2 - 39x - 126$
-
evaluate the following. $2.9 + 4.78 - 0.6^{2}$
7.32
-
evaluate the following. $2.3^{2}-0.3 \\times 4.6$
3.91
-
find the quotient and remainder using synthetic division: $\frac{x^{3}-…
The quotient is $x^2+3x+9$ The remainder is $4$
-
part i: definitions define the following terms using examples where app…
1. economic system: A societal framework for organizing resource use, production, and distribution of goods/services (e.g., the U.S. mixed economy). 2. market economy: An economic…
-
use synthetic division to divide $x^3 + 6x^2 + 10x + 11$ by $x + 1$ 1 6…
Synthetic division table filled: $-1$ $\bigg|$ $1$ $\quad$ $6$ $\quad$ $10$ $\quad$ $11$ $\quad$ $\bigg|$ $\quad$ $-1$ $\quad$ $-5$ $\quad$ $-5$ $\quad$ $\overline{\bigg|}$ $\over…
-
find the exact location of all the relative and absolute extrema of the…
$f$ has an absolute minimum (smallest x-value) at $(x,y)=(0, -9)$ $f$ has an absolute maximum (largest x-value) at $(x,y)=(3, 0)$ $f$ has a relative minimum at $(x,y)=(1, -12)$
-
use the graph of the function f shown to the right to answer parts (a)-…
$-24 < x < -4, 16 < x < 24$
-
14 mark for review $int sec x \tan x dx =$ a $sec x + c$ b $\tan x + c$…
A. $\sec x + C$
-
13 mark for review $int (e^{x}+e)dx =$ a $e^{x}+c$ b $2e^{x}+c$ c $e^{x…
E. $e^x+ex+C$
-
multiply. $square = 2.13 \\times 0.197$
$0.41961$
-
why did colonists oppose writs of assistance?(1 point)○ they thought it…
B. They thought it violated their rights.
-
graph these equations:$y = 4x - 5$$y = -1$click to select points on the…
1. For $y=4x-5$: Plot points $(0, -5)$ and $(2, 3)$, then draw a straight line through them. 2. For $y=-1$: Draw a horizontal straight line that passes through any point with a $y…
-
$59+25$ options: 94, 84, 79, 75
B. 84
-
$51+32$ options: 83, 88, 93, 94
A. 83
-
$65+28$ 60 5 20 8 95 93 88 84
93
-
62+19 60 + 20 + 1 + 9 20 + 90 + 6 + 1 60 + 10 + 2 + 9
60 + 10 + 2 + 9
-
$67+22$ options: 98, 89, 88, 99
B. 89
-
evaluate: $f(g(-7))$ $y = f(x)$ $y = g(x)$ answer attempt 1 out of 2
$-7$
-
let $f(x) = 2x^3 - 15x^2 + 24x - 2$. find the derivative. $f(x) = $the …
$f'(x) = 6x^2 - 30x + 24$ The smaller critical value equals $1$ and the larger one equals $4$
-
$50 + 10$ + $2 + 2$ $60 + 4$
64
-
1-6 do you understand? 1. essential question how does the equation of a…
1. The vertex form $f(x)=a(x-h)^2+k$ directly shows the vertex $(h,k)$ and the direction/width of the parabola from the value of $a$. 2. Martin made an error in the direction of t…
-
16. the graph of $f(x)=\\tan(bx)$, where $b$ is a constant, is shown in…
$\boldsymbol{\frac{\pi}{2}}$ (Option C) --- ### Question 17
-
36 + 27 30 + 20 + 6 + 7 50 + 13 63 36 + 27 =
63
-
evaluate the following. progress: 0/2 part 1 of 2 (a) $|5| - 9 = \\squa…
$-4$
-
3.8 the tangent function 3.8 test prep 15. the graph of the function g …
(D) II and III only
-
26. consider the linear function $f(x)=7x + 25$ and the exponential fun…
21
-
estimate the solution to the system of equations. you can use the inter…
B. $x = -1, y = 3\frac{2}{3}$ (note: the correct $y$-value is $2\frac{2}{3}$, likely a typo in the option)
-
$42 + 58 = \\square$
100
-
$\\begin{cases} -3x - 9y = 18 \\\\ 4x + 3y = 12 \\end{cases}$ $x = \\sq…
$x = 6$ $y = -4$
-
find: $f(-3)$ answer
-3
-
15 fill in the blank 1 point question 14 the graph shows two functions,…
$g(x) = f(x) - 3$
-
3 numeric 1 point given: $f(x)=\\begin{cases}x^{2}+1; & x\\leq -1 \\\\ …
-33
-
2 numeric 1 point given: $f(x)=\\begin{cases} -2x & \\text{if } x < -1 …
-22
-
1 numeric 1 point given $f(x)=\\begin{cases}-(x + 1)^2 + 1 & \\text{for…
1
-
evaluate: $f(g(7))$ $y = f(x)$ $y = g(x)$ answer attempt 2 out of 2
7
-
find the solution to the system of equations. you can use the interacti…
$x = -2$ $y = 5$
-
38 + 47 30 + 40 + 8 + 7
70 (for the empty bubble), final sum is 85
-
instructions: eval 3. a) $log_{6}36 = $ b) $log_{2}32 = $ c) $log_{4}64…
A) $2$ B) $5$ C) $3$ D) $4$
-
evaluate: $f(g(-6))$ $y = f(x)$ $y = g(x)$
$-6$
-
explore & reason the table represents a(x), the area of a square as a f…
A. $g(x) = 2x^2$ B. Each point of the new function is a vertical stretch of the corresponding point on $A(x)$ by a factor of 2 (the y-coordinate is twice as large for the same x-c…
-
the equation of the exponential function represented by the following t…
$y = 2(3)^x$
-
select all the correct answers. consider function f and function g. $f(…
- Unlike the graph of function $f$, the graph of function $g$ decreases as $x$ increases. - The graphs of both functions have a vertical asymptote of $x = 0$. - The graph of funct…
-
evaluate the function. put your answer in function notation. find $f(8)…
$f(8) = -286$
-
let $f$ and $g$ have continuous first and second derivatives everywhere…
C. III only
-
testing version staar desmos calculator graph the quadratic below in yo…
$x = \frac{1}{4}$, $x = -\frac{3}{2}$
-
complete the table and then graph the function. $f(x) = -5x$ | $x$ | $f…
Completed table: | $x$ | $f(x)$ | |-----|--------| | -2 | 10 | | 0 | 0 | | 1 | -5 | | 2 | -10 | Graph points: Plot $(-2, 10)$, $(0, 0)$, $(1, -5)$, $(2, -10)$ and draw a straight …
-
details no additional details were added for this assignment. view subm…
6
-
$v(t) = t^4 - 2t^3 - 4t$ what is the particles velocity $v(t)$ at $t = …
$v(1) = -5$ $a(1) = -6$ The particle is speeding up.
-
log with base \e\ ($\\log_e x$) is referred to as... common logarithm b…
natural logarithm
-
name ____ teacher ____ period ____topic 5 test: rational exponents and …
1. $3xy^3$ 2. $3\sqrt{2x}$ 3. C. $\sqrt[11]{121}$ 4. D. $y=-9+\sqrt{x-3}$ 5. B. $17^{\frac{4}{3}}$ 6. A. $(-x)^{-\frac{3}{5}}$ 7. $f^{-1}(x)=\pm\frac{\sqrt[6]{x+1}}{2}$ 8. (Graph …
-
svlc algebra iii - standard (15261) exponential growth functions gerald…
The conclusion is incorrect because the range is limited to the set of positive real numbers.
-
snc.algebra iii - standard (10/29)exponential growth functionsgeraldine…
1. Statement 1 is incorrect because the y-values are increased by 2, not doubled 2. Statement 2 is incorrect because the y-values are doubled, not halved 3. The conclusion is inco…
-
algebra 1b - standard 15281exponential growth functionsseveral ordered …
The domain is the set of real numbers, and the range is $y > 0$.
-
multiply. $70.6 \\times 53.9$
3805.34
-
8. a) on what intervals of x is $f(x)$ increasing? b) on what intervals…
a) $(-\infty, -1)$ b) $(-1, \infty)$ c) $(-\infty, -3)$ --- ### Problem 9
-
7 rewrite the following logs with base 10: $log_{26} 18 = square$ $log_…
$\log_{26} 18 = \frac{\log_{10} 18}{\log_{10} 26}$ $\log_{99} 32 = \frac{\log_{10} 32}{\log_{10} 99}$ $\log_{12} 4 = \frac{\log_{10} 4}{\log_{10} 12}$
-
1. click the button 2. type \log\ in the first box, then your base in t…
$b^e = a$
-
5. a) on what intervals of x is f(x) positive? b) on what intervals of …
a) $(-\infty, \infty)$ b) $(-\infty, \infty)$ c) $(-\infty, \infty)$ --- ### Problem 6
-
5. a) on what intervals of x is f(x) positive? b) on what intervals of …
a) $(-\infty, \infty)$ b) $(-\infty, \infty)$ c) $(-\infty, \infty)$ --- ### Problem 6
-
multiply. answer as a mixed number in simplest form. $2\\frac{1}{2} \\t…
$9\frac{1}{2}$ (The whole number part is 9)
-
multiply. answer as a mixed number in simplest form. $2\\frac{1}{2} \\t…
$9\frac{1}{2}$ (The whole number part is 9)
-
graph the equation. $y=2x+1$ use the graphing tool to graph the line. u…
The line passes through points such as $(0,1)$ and $(1,3)$, extending infinitely in both directions on the coordinate grid.
-
gebra ii sem 2 1.9.3 quiz: finding vertical asymptotes given the graph …
B. \(F(x)\) is a very large positive number
-
example there are 4 boxes of printer paper to be divided equally among …
Number Line A (the first number line marked with 0, 1, 2, 3, 4, with each whole divided into 6 equal segments)
-
exponential growth functions the graph represents the function $f(x) = …
- The graph will increase at a slower rate. - The y-values will continue to increase as x-increases.
-
how would the graph change if the $b$ value in the equation is decrease…
D. The graph will increase at a slower rate. E. The $y$-values will continue to increase as $x$-increases.
-
multiply. try using the cross-cancel strategy to simplify the problem. …
13
-
bra ii sem 2 1.9.3 quiz: finding vertical asymptotes question 7 of 10 w…
A. $f(x)=\frac{1}{x}$
-
multiply. try using the cross-cancel strategy to simplify the problem. …
13
-
1.9.3 quiz: finding vertical asymptotes question 6 of 10 for the functi…
A. -0.01 is **not** a valid value. The function $f(x)=\frac{1}{x}$ produces values with very large magnitude (positive or negative) when $x$ is close to 0. *Note: If other options…
-
what is the slope of this line? simplify your answer and write it as a …
$\frac{-4}{5}$
-
composite functions & inverses perform the indicated operation. 1) $f(x…
$f(g(x)) = 3x^2 - 9x - 2$ $g(f(x)) = 9x^2 - 21x + 10$
-
1.9.3 quiz: finding vertical asymptotes question 4 of 10 at what value …
C. 1
-
the graph represents the function $f(x) = 10(2)^x$ how would the graph …
- The y-values will each be less than their corresponding x values - The graph will increase at a slower rate - The y-values will continue to increase as x increases
-
ponential growth functions the graph represents the function $f(x)=10(3…
- The graph will increase at a slower rate - The y-values will continue to increase as x increases
-
which of the following correctly identifies the factor $k$ for the vert…
B. $k=\frac{1}{4}$
-
simplifying fractions grade 5 fractions worksheet simplify the fraction…
1. $\frac{1}{5}$ 2. $\frac{1}{2}$ 3. $\frac{1}{10}$ 4. $\frac{4}{5}$ 5. $\frac{3}{4}$ 6. $\frac{2}{3}$ 7. $\frac{1}{2}$ 8. $\frac{11}{12}$ 9. $\frac{1}{2}$ 10. $\frac{1}{5}$ 11. $…
-
upton sinclairs the jungleinvestigated ______ and brought about the pas…
1. the meat packing industry 2. censored
-
the graph represents the function $f(x) = 10(2)^x$ how would the graph …
- The y-values will each be less than their corresponding x values - The graph will increase at a slower rate - The y-values will continue to increase as x increases
-
consider the following two functions. original: $f(x)=|x| + 1$ final: $…
Option #2: a vertical compression
-
complete this assessment to review what youve learned identify the fact…
$\frac{1}{2}$
-
use the given zero to find all the zeros of the function. (enter your a…
For \(h(x) = 4x^3 - 13x^2 + 28x + 30\): \(2-\sqrt{6}i, 2+\sqrt{6}i, -\frac{3}{4}\) For \(f(x) = x^3 + 5x^2 + 24x + 20\): \(-2-4i, -2+4i, -1\)
-
graph the equation $y = x^2 + 4x + 3$ on the accompanying set of axes. …
The 5 points to plot are $(-4, 3)$, $(-3, 0)$, $(-2, -1)$, $(-1, 0)$, $(0, 3)$. The roots of $x^2 + 4x + 3 = 0$ are $x=-3$ and $x=-1$.
-
the graph represents the function $f(x) = 10(1.5)^x$ how would the grap…
- The graph will increase at a slower rate. - The y-values will continue to increase as x increases.
-
find the rate of change of the linear function shown in the graph. then…
Rate of change: $-\frac{1}{2}$ Initial value: $2$
-
ponential growth functions what are the domain and range of the functio…
The domain includes all real numbers, and the range is $y > 0$
-
what are the domain and range of the relation in the graph? the domain …
The domain includes all non-negative numbers, and the range is $y \geq 0$
-
question 1 of 3 select the correct answer from each drop-down menu. the…
The parent function of the function represented in the table is exponential. If function $f$ is vertically compressed by a factor of $\frac{1}{4}$, the $f(x)$-values will be divid…
-
bra 1b - standard (15261) tial growth functions ramon is graphing the f…
The fourth graph (with the point (0, 3) plotted)