Question 1

What is the long-run behavior of the function $y=\frac{(x-1)(x+4)}{e^{6 x}}$

Accepted Answer

As @#LAT-DLM& then @#LAT-DLM&.

Question 2

A $12 \mathrm{~kg}$ sample of a certain alloy (mixture of metals) contains $2 \mathrm{~kg}$ of tin and $10 \mathrm{~kg}$ of copper. A chemist decides to study the properties of the alloy as its percentage of tin is varied. Suppose $x$ represents the quantity of tin, in $\mathrm{kg}$, the chemist adds to the sample. Let $f(x)$ represent the fraction of the mixture's mass composed of tin--that is, the ratio of the tin's mass to the mixture's total mass. A negative value of $x$ represents a quantity of tin removed from the original $12 \mathrm{~kg}$ sample. What is the domain of $f$ ?

Accepted Answer

A)  All real numbers $x$. 
B)  All $x \geq 0$. 
C)  All $x \geq 2$. 
D)  All $x \geq-2$. 
E)  All $x \geq-12$. 
A)  All real numbers $x$. 
B)  All $x \geq 0$. 
C)  All $x \geq 2$. 
D)  All $x \geq-2$. 
E)  All $x \geq-12$.

Question 3

Can $f(x)=x^{3}\left(x^{4}\right)^{4}$ be written in the form of an exponential function, a power function, or neither?

Accepted Answer

A)  Neither 
B)  An exponential function 
C)  A power function 
A)  Neither 
B)  An exponential function 
C)  A power function

Question 4

When temperature is held constant, the pressure $P$ and volume $V$ of a quantity of gas are inversely proportional (Boyle's Law). The following figure shows this relationship for a particular gas. Find a formula for $V$ in terms of $P$ and use it to find $V$ when $P$ is 7 . Round to 2 decimal places.

Accepted Answer

The answer of When temperature is held constant, the pressure...

Question 5

Which of the following statements are true for $f(x)=\frac{x^{2}-25}{x^{2}+4 x}$ ? Mark all that apply.

Accepted Answer

A)  There is a horizontal asymptote at $y=1$. 
B)  There are horizontal asymptotes at $y=-5$ and 5 . 
C)  There are no horizontal asymptotes. 
D)  There is a vertical asymptote at $x=1$. 
E)  There are vertical asymptotes at $x=0$ and -4 .
F) There are no vertical asymptotes. 
A)  There is a horizontal asymptote at $y=1$. 
B)  There are horizontal asymptotes at $y=-5$ and 5 . 
C)  There are no horizontal asymptotes. 
D)  There is a vertical asymptote at $x=1$. 
E)  There are vertical asymptotes at $x=0$ and -4 .
F) There are no vertical asymptotes.

Question 6

The power function through the points $(1,6)$ and $(6,9)$ is $y=k x^{p}$, where $k=$ -----------and $p=\ldots$. Round the second answer to 3 decimal places.

Accepted Answer

The answer of The power function through the points $(1,6)$...

Question 7

Which of the following statements are true for $f(x)=\frac{-11(x-3)(x+6)}{(x+5)(x-7)}$ ? Mark all that apply.

Accepted Answer

A)  The $x$ - intercepts are -6 and 3 . 
B)  The $x$ - intercepts are -5 and 7 . 
C)  There are no $x$-intercepts. 
D)  The $y$-intercept is $-\frac{198}{35}$. 
E)  The $y$-intercepts are -5 and 7 .
F) There are no $y$-intercepts. 
A)  The $x$ - intercepts are -6 and 3 . 
B)  The $x$ - intercepts are -5 and 7 . 
C)  There are no $x$-intercepts. 
D)  The $y$-intercept is $-\frac{198}{35}$. 
E)  The $y$-intercepts are -5 and 7 .
F) There are no $y$-intercepts.

Question 8

The domain of the function $y=\ln \left((2 x-3) x^{2}\right)$ is

Accepted Answer

A)  all $x>0$ except for $x=\frac{3}{2}$ 
B)  all $x>\frac{3}{2}$ 
C)    
D)  all $x>0$ 
A)  all $x>0$ except for $x=\frac{3}{2}$ 
B)  all $x>\frac{3}{2}$ 
C)    
D)  all $x>0$

Question 9

Use a graphing calculator or computer to graph $y=x^{4}+2 x^{3}-7 x^{2}-8 x+12$. Use the graph to pick the factored form of $y$.

Accepted Answer

A)  $y=(x-2)(x+1)(x+3)(x+2)$ 
B)  $y=(x-2)(x-1)(x+3)(x+2)$ 
C)  $y=(x+2)(x+1)(x-3)(x-2)$ 
D)  $y=(x-2)(x-1)(x-3)(x+2)$ 
A)  $y=(x-2)(x+1)(x+3)(x+2)$ 
B)  $y=(x-2)(x-1)(x+3)(x+2)$ 
C)  $y=(x+2)(x+1)(x-3)(x-2)$ 
D)  $y=(x-2)(x-1)(x-3)(x+2)$

Question 10

Which of the following are possible formulas for a fourth degree polynomial with at least one zero at $x=-4$, a double zero at $x=3$, and long-run behavior: as $x \rightarrow \infty, y \rightarrow-\infty$. .

Accepted Answer

A)  $y=-2(x+4)(x-6)(x-3)^{2}$ 
B)  $y=2(x+4)(x-6)(x-3)^{2}$ 
C)  $y=-(x+4)^{2}(x-3)^{2}$ 
D)  $y=-a(x+4)(x-6)(x-3)^{2}$ where $a>0$ 
A)  $y=-2(x+4)(x-6)(x-3)^{2}$ 
B)  $y=2(x+4)(x-6)(x-3)^{2}$ 
C)  $y=-(x+4)^{2}(x-3)^{2}$ 
D)  $y=-a(x+4)(x-6)(x-3)^{2}$ where $a>0$

Question 11

Can $f(x)=2 x \cdot 3^{1-x}$ be written in the form of an exponential function, a power function, or neither?

Accepted Answer

A)  Neither 
B)  A power function 
C)  An exponential function 
A)  Neither 
B)  A power function 
C)  An exponential function

Question 12

Does the function $f(x)=2 x^{4}+5 x-10$ have a minimum value?

Accepted Answer

A) True 
 B)False

Question 13

Compute the following limits:
a) $\lim _{x \rightarrow \infty}\left(5 x^{3}+9 x-117\right)$
b) $\lim _{x \rightarrow-\infty}\left(5 x^{3}+9 x-117\right)$

Accepted Answer

The answer of Compute the following limits:
a) \(\lim _{x \rightarrow...

Question 14

A polynomial with integer coefficients having $\frac{3+\sqrt{3}}{7}$ as a zero is $f(x)=a x^{2}+b x+c$, where $a=\ldots, b=\ldots$, and $c=\ldots$. Make your value for $a$ be positive and as small as possible.

Accepted Answer

Part A: 49

Question 15

Let $f(x)=\frac{2+x}{5-9 x}$. Find $f^{-1}(x)$.

Accepted Answer

The answer of Let $f(x)=\frac{2+x}{5-9 x}$. Find $f^{-1}(x)$....

Question 16

Which of the following functions dominates as $x \rightarrow \infty$ ?

Accepted Answer

A)  $y=(10 x)^{1.35}$ 
B)  $y=1.35^{x}$ 
A)  $y=(10 x)^{1.35}$ 
B)  $y=1.35^{x}$

Question 17

The formula for the exponential function shown in the following table is $g(x)=a b^{x}$, where $a=$----------- and $b=$------------- Round both answers to 2 decimal places.

Accepted Answer

The answer of The formula for the exponential function shown...

Question 18

Find the formula for a third degree polynomial with a zero at $x=-5$, a double zero at $x=3$, and $y$-intercept at -135 .

Accepted Answer

The answer of Find the formula for a third degree...

Question 19

Is $y=(x-3)(x+3)$ a power function?

Accepted Answer

A) True 
 B)False

Question 20

The ant population in a sandbox has been modelled by the following function: $y=343-9.5 x^{2}+102.7 x$ where $x$ is the number of months after January 2010 .
a) How many ants are in the sandbox in January 2010 ?
b) How many ants are predicted to be in the sandbox in February 2011 ?

Accepted Answer

a) There are 343 ants in the s

What is the long-run behavior of the function $y=\frac{(x-1)(x+4)}{e^{6 x}}$

Can $f(x)=x^{3}\left(x^{4}\right)^{4}$ be written in the form of an exponential function, a power function, or neither?

Which of the following statements are true for $f(x)=\frac{x^{2}-25}{x^{2}+4 x}$ ? Mark all that apply.

The power function through the points $(1,6)$ and $(6,9)$ is $y=k x^{p}$ , where $k=$ -----------and $p=\ldots$ . Round the second answer to 3 decimal places.

Which of the following statements are true for $f(x)=\frac{-11(x-3)(x+6)}{(x+5)(x-7)}$ ? Mark all that apply.

The domain of the function $y=\ln \left((2 x-3) x^{2}\right)$ is

Use a graphing calculator or computer to graph $y=x^{4}+2 x^{3}-7 x^{2}-8 x+12$ . Use the graph to pick the factored form of $y$ .

Which of the following are possible formulas for a fourth degree polynomial with at least one zero at $x=-4$ , a double zero at $x=3$ , and long-run behavior: as $x \rightarrow \infty, y \rightarrow-\infty$ . .

Can $f(x)=2 x \cdot 3^{1-x}$ be written in the form of an exponential function, a power function, or neither?

Does the function $f(x)=2 x^{4}+5 x-10$ have a minimum value?

Compute the following limits: a) $\lim _{x \rightarrow \infty}\left(5 x^{3}+9 x-117\right)$ b) $\lim _{x \rightarrow-\infty}\left(5 x^{3}+9 x-117\right)$

A polynomial with integer coefficients having $\frac{3+\sqrt{3}}{7}$ as a zero is $f(x)=a x^{2}+b x+c$ , where $a=\ldots, b=\ldots$ , and $c=\ldots$ . Make your value for $a$ be positive and as small as possible.

Let $f(x)=\frac{2+x}{5-9 x}$ . Find $f^{-1}(x)$ .

Which of the following functions dominates as $x \rightarrow \infty$ ?

Find the formula for a third degree polynomial with a zero at $x=-5$ , a double zero at $x=3$ , and $y$ -intercept at -135 .

Is $y=(x-3)(x+3)$ a power function?

The ant population in a sandbox has been modelled by the following function: $y=343-9.5 x^{2}+102.7 x$ where $x$ is the number of months after January 2010 . a) How many ants are in the sandbox in January 2010 ? b) How many ants are predicted to be in the sandbox in February 2011 ?

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Exam 11: Polynomial and Rational Functions

What is the long-run behavior of the function y=(x−1)(x+4)e6xy=\frac{(x-1)(x+4)}{e^{6 x}}y=e6x(x−1)(x+4)​

Can f(x)=x3(x4)4f(x)=x^{3}\left(x^{4}\right)^{4}f(x)=x3(x4)4 be written in the form of an exponential function, a power function, or neither?

Which of the following statements are true for f(x)=x2−25x2+4xf(x)=\frac{x^{2}-25}{x^{2}+4 x}f(x)=x2+4xx2−25​ ? Mark all that apply.

The power function through the points (1,6)(1,6)(1,6) and (6,9)(6,9)(6,9) is y=kxpy=k x^{p}y=kxp , where k=k=k= -----------and p=…p=\ldotsp=… . Round the second answer to 3 decimal places.

Which of the following statements are true for f(x)=−11(x−3)(x+6)(x+5)(x−7)f(x)=\frac{-11(x-3)(x+6)}{(x+5)(x-7)}f(x)=(x+5)(x−7)−11(x−3)(x+6)​ ? Mark all that apply.

The domain of the function y=ln⁡((2x−3)x2)y=\ln \left((2 x-3) x^{2}\right)y=ln((2x−3)x2) is

Use a graphing calculator or computer to graph y=x4+2x3−7x2−8x+12y=x^{4}+2 x^{3}-7 x^{2}-8 x+12y=x4+2x3−7x2−8x+12 . Use the graph to pick the factored form of yyy .

Which of the following are possible formulas for a fourth degree polynomial with at least one zero at x=−4x=-4x=−4 , a double zero at x=3x=3x=3 , and long-run behavior: as x→∞,y→−∞x \rightarrow \infty, y \rightarrow-\inftyx→∞,y→−∞ . .

Can f(x)=2x⋅31−xf(x)=2 x \cdot 3^{1-x}f(x)=2x⋅31−x be written in the form of an exponential function, a power function, or neither?

Does the function f(x)=2x4+5x−10f(x)=2 x^{4}+5 x-10f(x)=2x4+5x−10 have a minimum value?

Compute the following limits: a) lim⁡x→∞(5x3+9x−117)\lim _{x \rightarrow \infty}\left(5 x^{3}+9 x-117\right)limx→∞​(5x3+9x−117) b) lim⁡x→−∞(5x3+9x−117)\lim _{x \rightarrow-\infty}\left(5 x^{3}+9 x-117\right)limx→−∞​(5x3+9x−117)

A polynomial with integer coefficients having 3+37\frac{3+\sqrt{3}}{7}73+3​​ as a zero is f(x)=ax2+bx+cf(x)=a x^{2}+b x+cf(x)=ax2+bx+c , where a=…,b=…a=\ldots, b=\ldotsa=…,b=… , and c=…c=\ldotsc=… . Make your value for aaa be positive and as small as possible.

Let f(x)=2+x5−9xf(x)=\frac{2+x}{5-9 x}f(x)=5−9x2+x​ . Find f−1(x)f^{-1}(x)f−1(x) .

Which of the following functions dominates as x→∞x \rightarrow \inftyx→∞ ?

The formula for the exponential function shown in the following table is g(x)=abxg(x)=a b^{x}g(x)=abx , where a=a=a= ----------- and b=b=b= ------------- Round both answers to 2 decimal places.

Find the formula for a third degree polynomial with a zero at x=−5x=-5x=−5 , a double zero at x=3x=3x=3 , and yyy -intercept at -135 .

Is y=(x−3)(x+3)y=(x-3)(x+3)y=(x−3)(x+3) a power function?

Linear Functions and Change

Functions

Quadratic Functions

Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Compositions, Inverses, and Combinations of Functions

Vectors and Matrices

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Filters

What is the long-run behavior of the function $y=\frac{(x-1)(x+4)}{e^{6 x}}$

Can $f(x)=x^{3}\left(x^{4}\right)^{4}$ be written in the form of an exponential function, a power function, or neither?

Which of the following statements are true for $f(x)=\frac{x^{2}-25}{x^{2}+4 x}$ ? Mark all that apply.

The power function through the points $(1,6)$ and $(6,9)$ is $y=k x^{p}$ , where $k=$ -----------and $p=\ldots$ . Round the second answer to 3 decimal places.

Which of the following statements are true for $f(x)=\frac{-11(x-3)(x+6)}{(x+5)(x-7)}$ ? Mark all that apply.

The domain of the function $y=\ln \left((2 x-3) x^{2}\right)$ is

Use a graphing calculator or computer to graph $y=x^{4}+2 x^{3}-7 x^{2}-8 x+12$ . Use the graph to pick the factored form of $y$ .

Which of the following are possible formulas for a fourth degree polynomial with at least one zero at $x=-4$ , a double zero at $x=3$ , and long-run behavior: as $x \rightarrow \infty, y \rightarrow-\infty$ . .

Can $f(x)=2 x \cdot 3^{1-x}$ be written in the form of an exponential function, a power function, or neither?

Does the function $f(x)=2 x^{4}+5 x-10$ have a minimum value?

Compute the following limits: a) $\lim _{x \rightarrow \infty}\left(5 x^{3}+9 x-117\right)$ b) $\lim _{x \rightarrow-\infty}\left(5 x^{3}+9 x-117\right)$

A polynomial with integer coefficients having $\frac{3+\sqrt{3}}{7}$ as a zero is $f(x)=a x^{2}+b x+c$ , where $a=\ldots, b=\ldots$ , and $c=\ldots$ . Make your value for $a$ be positive and as small as possible.

Let $f(x)=\frac{2+x}{5-9 x}$ . Find $f^{-1}(x)$ .

Which of the following functions dominates as $x \rightarrow \infty$ ?

Find the formula for a third degree polynomial with a zero at $x=-5$ , a double zero at $x=3$ , and $y$ -intercept at -135 .

Is $y=(x-3)(x+3)$ a power function?