微積分
極限、導數、最優化與函數性質。
-
solve the following exponential equation. express the solution set in t…
\(2.71\)
-
question factor to find all x-intercepts of the function. $f(x) = x^3 -…
\( x = -2, 2, 3 \)
-
write down the first five terms of the sequence $a_n = \\frac{(n + 1)!}…
\(a_1 = \boldsymbol{\frac{1}{6}}\) \(a_2 = \boldsymbol{\frac{3}{11}}\) \(a_3 = \boldsymbol{\frac{2}{3}}\) \(a_4 = \boldsymbol{\frac{20}{9}}\) \(a_5 = \boldsymbol{\frac{180}{19}}\)
-
question 10 of 10 how does the graph of $f(x) = \\frac{1}{2}(3)^{x + 2}…
A. The parent function has been translated down. C. The parent function has been translated to the left. D. The parent function has been compressed.
-
determine the equation of the line that passes through the given points…
C. \(y = 2\)
-
add. \\frac{5}{6} + \\frac{2}{3} = submit
$\frac{3}{2}$ (or $1\frac{1}{2}$)
-
evaluate the expression without using a calculator. \\ln e^{6} \\ln e^{…
6
-
an expression is shown. \\(\\frac{5}{12} \\div \\frac{1}{3}\\) what is …
C. $\frac{5}{4}$
-
for the exponential equation $2^{x + 3} = 37$, complete parts a) and b)…
A. The exact solution to the equation \(2^{x + 3}=37\) using natural logarithms is \(x=\frac{\ln(37)}{\ln(2)}-3\). ### Part b)
-
given the function f(x) = (x + 8)^3, complete parts a through c. (a) fi…
\( \sqrt[3]{x}-8 \)
-
find equations for the vertical asymptotes, if any, for the following r…
none
-
consider the following polynomial. $f(x) = x^2(x + 5)(x - 9)$ step 2 of…
For \(f(x) ightarrow\) \(\boldsymbol{\infty}\) as \(x ightarrow-\infty\) For \(f(x) ightarrow\) \(\boldsymbol{\infty}\) as \(x ightarrow\infty\)
-
solve the following elementary exponential equation. $9^{-x} = 3$ answe…
\(x = -\frac{1}{2}\)
-
find equations for the horizontal asymptotes, if any, for the following…
\( y = 0 \)
-
use technology to find points and then graph the following polynomial, …
\( f(x) = (x - 2)(x - 4)(x + 4)(x + 6) \) (or \( (x - 2)(x + 2)(x + 4)(x + 6) \) is incorrect, correct is \( (x - 2)(x - 4)(x + 4)(x + 6) \) after proper factoring)
-
directions: use the drawing tool(s) to form the correct answers on the …
The two consecutive points are 34.2 and 34.3. On the number line, plot a point on 34.2 and a point on 34.3 (using the 'Point' tool from the drawing tools as instructed).
-
the graph of $f(x) = 2^x + 1$ represents the growth of a population of …
\( 7.5 \)
-
name: 10) solve the inequality and graph its solution 2x + 4 ≥ 24 4 4
The solution to the inequality \( 2x + 4 \geq 24 \) is \( x \geq 10 \). To graph this solution, we draw a number line, place a closed circle at 10 (since the inequality is "greate…
-
the temperature dropped 3° per hour. how much did the temperature drop …
s: ## Temperature Drop: - A. 2 hours: \( 6^\circ\text{F} \) - B. 4 hours: \( 12^\circ\text{F} \) - C. 7 hours: \( 21^\circ\text{F} \) - D. 5 hours: \( 15^\circ\text{F} \) - E. \( …
-
name period ____ date ____ aim: how do we define and identify numbers a…
- $\sqrt{49}=\boldsymbol{7}$ (Integer, Yes) - $\sqrt{\frac{49}{196}}=\boldsymbol{\frac{1}{2}}$ (Fraction, Yes) - $\frac{\sqrt{144} + 200}{\sqrt{4}}=\boldsymbol{106}$ (Integer, Yes…
-
given that $g(x) = f(x) + k$, identify the value of $k$ for the functio…
\( k=-2 \)
-
drag the key features to the correct location on the image. each key fe…
- \( f(x)=\frac{-2x + 4}{x - 6} \): domain \( (-\infty,6)\cup(6,\infty) \), horizontal asymptote \( y=-2 \) - \( g(x)=\frac{x^{2}-2x}{x^{2}+x - 6} \): domain \( (-\infty,-3)\cup(-…
-
question 38 what is 3!? select one ○ 6 ○ 9 ○ 4 ○ 12
A. 6
-
arithmetic series: 7. a) determine the sum of the first 16 terms of the…
The sum of the first 16 terms is 6104.
-
a table of values of a linear function is shown below. | x | -3 | 0 | 3…
y-intercept: \(-5\) slope: \(1\)
-
3. the graph of $y = -sqrt{x}$ is shifted 2 units up and 5 units left. …
A. \( y = -\sqrt{x + 5} + 2 \)
-
question 34 which graph is correct for the inequality y < x + 2? select…
The third graph (assuming the graphs are listed from top to bottom as first, second, third, fourth)
-
1 the graph of $y = -sqrt{x}$ is shifted 4 units up and 3 units right. …
The second option (from the left) \( y = -\sqrt{x - 4}+3 \) (Wait, let's re - solve it properly) Wait, the original function is \( y=-\sqrt{x} \). Shifting 3 units right: for a ho…
-
1. the graph of $y = -sqrt{x}$ is shifted 4 units up and 3 units right.…
B. \( y = -\sqrt{x - 4} + 3 \)
-
quiz: graphing radical functions hs: algebra 2b m (sequential) / 2 inve…
The second option (the one with \( y = 3\sqrt{x - 4}-4 \) and description about translation 4 units right and 4 units down)
-
3. rewrite $y = \\sqrt{25x - 125} + 5$ to make it easy to graph using a…
\(y = 5\sqrt{x - 5}+5\) It is the graph of \(y = 5\sqrt{x}\) translated 5 units right and 5 units up
-
graph the system of linear inequalities. y ≥ 1 y < 2x + 1
The Middle Graph (the second graph from the top among the four given graphs)
-
1. choose the correct graph of the function $y = 2\\sqrt{x}$
The Top Graph
-
which equation can be used to verify that 99 ÷ 11 = 9? ○ 99 - 11 = 88 ○…
\( 9 \times 11 = 99 \) (the third option in the list)
-
write a function in any form that would match the graph shown below. (g…
\(y =-\frac{1}{2}(x + 5)(x - 4)^2\) (or the expanded form \(y=-\frac{1}{2}x^{3}+\frac{3}{2}x^{2}+12x - 40\))
-
(left(2\frac{5}{8} + 2\frac{1}{2} ight))
\(5\frac{1}{8}\)
-
guided practice graphing radical functions rewrite ( y = sqrt{4x + 20} …
C. Rewritten, \( y = 2\sqrt{x + 5}+5 \). It is the graph of \( y = 2\sqrt{x} \) translated 5 units left and 5 units up.
-
guided practice choose the correct graph of the function $y = 2\\sqrt3{…
B. The graph of option B
-
guided practice choose the correct graph of the function $y = \\sqrt3{x…
A. The graph of \( y = \sqrt[3]{x - 4} + 3 \)
-
identifying differences between multiplication and division sort each t…
For Whole Number Multiplication: "joining groups of equal size", "the same as repeated addition", "the inverse of division" For Whole Number Division: "splitting into equal - size…
-
guided practice choose the correct graph of the function $y = -\frac{1}…
A. (Assuming the first graph (A) is the correct one after analyzing the function's transformations. Wait, let's re - evaluate. Wait, the function is \(y =-\frac{1}{2}\sqrt{x - 3}-…
-
f(x) = log(|x + 4|) - 10 asymptote: domain: range: end behavior:
s: - Asymptote: \( \boldsymbol{x=-4} \) - Domain: \( \boldsymbol{(-\infty,-4)\cup(-4,\infty)} \) - Range: \( \boldsymbol{(-\infty,\infty)} \) - End Behavior: As \( \boldsymbol{x i…
-
9. $h(x) = \\frac{5x^3 - 7x^2 - x + 3}{x^8 - x^7 - 167x^6 - 395x^5 + 23…
The function \( h(x) \) is a rational function. The numerator factors as \( (x - 1)^{2}(5x + 3) \). Further analysis of the denominator (to find its roots and factors) can be done…
-
analyze the functions c(x) and b(x) to determine which has fewer zeros.…
Function \( c(x) \) has fewer zeros.
-
select the two correct answers. which expressions have a value between …
\(-2\sqrt{2.2}\), \(1 - \pi\) (i.e., the options with \(-2\sqrt{2.2}\) and \(1 - \pi\))
-
9. the exact answer to the equation $7^{3x} = 60$ is found as follows: …
\( x \approx 0.605 \)
-
part a what are the x - and y-intercepts of the graph of 9x - 7y = -63?…
## Part A x - intercept: \( (-7, 0) \) y - intercept: \( (0, 9) \) ## Part B The correct graph is Graph B (assuming Graph B is the one with positive slope passing through (0,9) an…
-
module 6: mastery mi algebra ii - s1 / module 6 / lesson 90 3. using a …
1. $\frac{\log 9}{4}\approx0.239$ (matches d) 2. $\frac{\ln 8}{7}\approx0.297$ (matches a) 3. $\frac{\log 4}{\log 6}\approx0.774$ (matches b) 4. $\frac{\ln 7}{2\ln 9}\approx0.443$…
-
for each line, determine whether the slope is positive, negative, zero,…
Line 1: Undefined Line 2: Positive Line 3: Zero Line 4: Negative
-
10 multiple choice 10 points what is the slope of the line through the …
\(-\frac{3}{5}\) (corresponding to the option with \(-\frac{3}{5}\))
-
8 multiple choice 10 points which best represents the transformation fr…
\(g(x)\) is shifted down 4 units and is \(1/3\) as steep
-
select the two correct answers. which expressions have a value between …
\(-2\sqrt{2.2}\) (value \(\approx - 2.966\) between \(-3\) and \(-2\)), \(1 - \pi\) (value \(\approx - 2.14\) between \(-3\) and \(-2\))
-
a neighborhood fair in texas, somewhere between the german oom - pah sa…
Nye relates a story about something she heard to emphasize the point she wants to make about heritage.
-
which set is ordered from least to greatest? a. $\\sqrt{2}$, $\\sqrt{\\…
D. \(5 - \pi^2\), \(\sqrt{\frac{1}{2}}\), \(\sqrt{2}\)
-
a wire is 7.5 feet long. it is divided into 2 pieces of equal length, a…
3.5
-
open desmos in another window so you can use it to plot points and writ…
B. \( y = 2x + 3 \)
-
simplify. \\sqrt4{\frac{1}{81}} be sure to write your answer in lowest …
$\frac{1}{3}$
-
3 the graph above represents what type of function? a. neither linear n…
D. nonlinear
-
simplify. \\sqrt3{\frac{343}{64}} be sure to write your answer in lowes…
$\frac{7}{4}$
-
1. (ma.912.ar.4.3) part a: use the table below to graph the absolute va…
The vertex is \(\boldsymbol{(2,-5)}\). The y - intercept is \(\boldsymbol{(0,-3)}\). The x - intercepts are \(\boldsymbol{(-3,0)}\) and \(\boldsymbol{(7,0)}\). ### Problem 2
-
opic 2 assessment form a slope: -4/3 slope: -3/4 slope: 4/3
slope: \(-\frac{3}{4}\) (assuming the top graph is the one with this slope)
-
u4: absolute value fct exit ticket describe the transformation: 15) $f(…
right 1 unit and down 2 units (the last option in the dropdown: "right 1 unit and down 2 units")
-
simplify. \\sqrt4{\frac{16}{625}} be sure to write your answer in lowes…
\(\frac{2}{5}\)
-
5. $e(x) = \\frac{x - 2}{x^3 - 172x - 336}$
\(e(x)=\frac{x - 2}{(x - 14)(x + 12)(x + 2)}\) (or if we consider factoring the denominator completely as above)
-
u4: absolute value fct exit ticket match the vertex to each absolute va…
9) \( f(x) = |x + 3| + 3 \) matches with \((-3, 3)\) 10) \( f(x) = |x| - 4 \) matches with \((0, -4)\) 11) \( f(x) = |x + 1| - 4 \) matches with \((-1, -4)\) 12) \( f(x) = |x - 2|…
-
describe the transformation: 15) $f(x) = |x - 1| - 2$
The graph of \( f(x) = |x| \) is shifted 1 unit to the right and 2 units down to get \( f(x) = |x - 1| - 2 \).
-
what country agreed to the 1907 gentlemen’s agreement, limiting the emi…
C. Japan
-
u4: absolute value fct exit ticket describe the transformation: 15) $f(…
15) down 2 units and right 1 unit (or 15) right 1 unit and down 2 units, as both describe the transformation of \( f(x)=|x - 1|-2 \) from \( y = |x| \))
-
3. find the equation of a line that passes through the point (7, -4) an…
\( y=\frac{1}{7}x - 5 \)
-
consider the following example of the logical fallacy of limited choice…
B. Premise: He refused to testify by invoking his Fifth Amendment rights. Conclusion: He must be guilty.
-
during the 1920s, how did the growth of immigrant populations in cities…
D. Many Americans in rural areas felt that their way of life was being threatened
-
use the four graphs shown below to answer questions 13-15. 13. lora got…
Graph A ### Question 14:
-
which statement is false? ○ the space race’s goal encouraged growth and…
The media presented the Space Race in technological and scientific terms only few understood.
-
a candle has been burning for 20 min and is now 25 cm tall. in an hour …
D. \( y - 25=-0.25(x - 20) \)
-
what are the equations of the horizontal and vertical asymptotes of $y …
horizontal asymptote: \( y = -7 \) vertical asymptote: \( x = 9 \)
-
how would you describe the difference between the graphs of $f(x) = 2x^…
A. \( g(x) \) is a reflection of \( f(x) \) over the \( x \)-axis.
-
what is the equation of the horizontal asymptote of $y = \\frac{9}{x + …
\( y=-6 \)
-
move the graphs that represent f(x) and g(x) into the table function\tg…
For \( f(x) = \log_2(x - 2) \), the graph is the increasing logarithmic graph with vertical asymptote \( x = 2 \), passing through \( (3, 0) \) and \( (4, 1) \) (e.g., the second …
-
find the inverse of the function. h(x) = x - 9 write your answer in the…
\( h^{-1}(x)=x + 9 \)
-
find the inverse of the function. \\( h(x) = \\frac{3x + 3}{-5x - 3} \\…
\( \frac{-3x - 3}{5x + 3} \) (or equivalent forms like \( \frac{-3(x + 1)}{5x + 3} \))
-
question 7 of 10 what can you say about the y-values of the two functio…
B. The minimum \( y \)-value of \( g(x) \) approaches \( -3 \)
-
match the graphs that represent ( f(x) ) and ( g(x) ) to the table. | f…
- For \( f(x) = 3\ln x \): The Rightmost Graph. - For \( g(x)=\log_{2}x \): The Second Graph (from the left).
-
find the inverse of the function. $f(x) = x^3 + 5$ write your answer in…
\( \sqrt[3]{x - 5} \) (or in the form \( 1\cdot\sqrt[3]{1x - 5}+0 \))
-
is the function c(x) even, odd, or neither? c(x)
even
-
what can you say about the end behavior of the function ( f(x) = 5x^3 -…
A. The leading coefficient is positive so the left end goes down, D. \( f(x) \) is an odd function so both ends go in opposite directions (Note: The function is not odd, but the e…
-
which of the following statements are true? graph of two functions f(x)…
B. Both graphs have exactly one asymptote.
-
below is the graph of $f(x) = \\ln(x)$. how would you describe the grap…
B. \( g(x) \) compresses \( f(x) \) by a factor of \( \frac{1}{3} \)
-
the function g(x) is a transformation of the parent function f(x). deci…
B. Horizontal or vertical stretch
-
question 7 (1 point) solve the equation \\(\\log(x + 6) - \\log(2x + 1)…
b) \(x=\frac{2}{7}\)
-
what can you say about the continuous function that generated the follo…
B. The function has at least one x - intercept.
-
adam put $100 in a savings account. after 10 years, he had $1649 in the…
A. 28%
-
which function could produce the graph shown below? a. $f(x) = 4e^{-0.5…
B. \( f(x)=4e^{-0.05x} \)
-
1.9 rational functions & vertical asymptotes ap precalculus name: ca #2…
1. Para \( f(x)=\frac{x^{2}-25}{x^{2}-8x + 15} \), la asíntota vertical es \( x = 3 \) (y un agujero en \( x = 5 \)) 2. Para \( g(x)=\frac{(x + 1)(x - 4)}{x^{2}-8x + 16} \), la as…
-
question 6 (1 point) solve for x: \\(\\log_x 16 = \\frac{4}{5}\\) \\(\\…
a) 32
-
1.9 rational functions & vertical asymptotes ap precalculus name: ca #2…
1. Vertical asymptote de \( f(x) \): \( \boldsymbol{x = 3} \) 2. Vertical asymptote de \( g(x) \): \( \boldsymbol{x = 4} \) 3. Vertical asymptotes de \( h(t) \): \( \boldsymbol{t …
-
use the image to answer the question. create a piecewise function that …
\( f(x)=\begin{cases}1, & -3\leq x < -1 \\ 2x - 1, & -1\leq x \leq 1\end{cases} \) (the first option among the given choices)
-
use the slope - intercept form to graph the equation $y = -2x - 1$ use …
To graph \( y = -2x - 1 \): 1. Plot the y-intercept \( (0, -1) \). 2. Use the slope \( -2 \) (rise -2, run 1) to find another point (e.g., \( (1, -3) \) or \( (-1, 1) \)). 3. Draw…
-
the table shows values of a square root function, f(x). | x | 0 | 1 | 4…
The y - intercept of \( f(x) \) is equal to the y - intercept of \( g(x) \). The minimum value of \( f(x) \) is greater than the minimum value of \( g(x) \). So the first blank is…
-
write the equation of the trigonometric function shown in the graph. y …
\( y = 1 \sin(1x) + 0 \) (or simplified as \( y = \sin(x) \))
-
question 7 of 10 what is the solution to the equation below? round your…
D. $x = 1.22$