Question 1

The curve W = f(t), given in the graph below, comes from the Wall Street Journal, September 4, 1992.W is a function.

Accepted Answer

A) True 
 B)False

Question 2

Temperatures in Town A oscillate daily between 30° F at 4am and 60° F at 4pm.The temperature in Town B is consistently 10° F colder than in Town A.What does the formula $H=-15 \cos \left(\frac{\pi}{12} t\right)+45$
 represent?

Accepted Answer

A) Temperature in Town A, in terms of time where time is measured in hours from 4am. 
B) Temperature in Town B, in terms of time where time is measured in hours from 4am. 
C) Temperature in Town A, in terms of time where time is measured in hours from 4pm. 
D) Temperature in Town B, in terms of time where time is measured in hours from 4pm. 
A) Temperature in Town A, in terms of time where time is measured in hours from 4am. 
B) Temperature in Town B, in terms of time where time is measured in hours from 4am. 
C) Temperature in Town A, in terms of time where time is measured in hours from 4pm. 
D) Temperature in Town B, in terms of time where time is measured in hours from 4pm.

Question 3

Graphically find a solution to the equation $6^{x}=x^{6}$
 in the interval $[-1 \leq x \leq 1]$
 .Give your answer accurate to 2 decimal places.

Accepted Answer

The answer of Graphically find a solution to the equation...

Question 4

Is the function $\frac{1}{\sqrt{x^{2}-9}}$
 continuous on the interval $0 \leq x \leq 4$
 ?

Accepted Answer

A) True 
 B)False

Question 5

Use the following figure to give the approximate value (to the nearest integer)of $\lim _{x \rightarrow-4} f(x)$
 .If the limit does not exist, enter "DNE".

Accepted Answer

The answer of Use the following figure to give the...

Question 6

The graph of a function y = f(x)is given below.Sketch a graph of it's inverse function on the same axes.

Accepted Answer

The answer of The graph of a function y =...

Question 7

Suppose f(x)and g(x)are both increasing functions.
a)Must f(g(x))be an increasing function? If so, explain why.If not, give an example.
b)Must f(g(x))be invertible? If so explain why.If not, give an example.

Accepted Answer

Answers will vary.One example is given b

Question 8

On the $x-$
 interval between E and F, the function graphed below is:   Mark all that apply.

Accepted Answer

A) increasing 
B) decreasing 
C) concave up 
D) concave down 
A) increasing 
B) decreasing 
C) concave up 
D) concave down

Question 9

Given the graphs of $y=g(x)$
 and $y=f(x)$
 in the following figure, estimate g(f(5)).

Accepted Answer

The answer of Given the graphs of $y=g(x)$
 and $y=f(x)$
...

Question 10

Find $\lim _{x \rightarrow 0} \frac{1}{6 x^{2}}$
 if it exists.

Accepted Answer

A)  $\frac{1}{6}$ 
B)  42 
C) 1 
D)  $\frac{1}{7}$ 
E) DNE 
A)  $\frac{1}{6}$ 
B)  42 
C) 1 
D)  $\frac{1}{7}$ 
E) DNE

Question 11

Given the function $y=f(x)=\frac{8}{5 x-8}$
 , give a formula for the inverse function of f(x).

Accepted Answer

The answer of Given the function $y=f(x)=\frac{8}{5 x-8}$
 , give...

Question 12

Find the equation for the line L shown below.

Accepted Answer

A)  $y=b\left(x+1-e^{b}\right)$ 
B)  $y=\frac{b}{e^{b}-1}(x-1)$ 
C)  $y=\frac{b}{b-e^{b}}\left(x-e^{b}\right)$ 
D)  $y=\frac{b}{e^{b}-e}(x-e)$ 
A)  $y=b\left(x+1-e^{b}\right)$ 
B)  $y=\frac{b}{e^{b}-1}(x-1)$ 
C)  $y=\frac{b}{b-e^{b}}\left(x-e^{b}\right)$ 
D)  $y=\frac{b}{e^{b}-e}(x-e)$

Question 13

Write a formula representing the function that says: The circumference of a circle is proportional to the diameter of the circle.

Accepted Answer

The answer of Write a formula representing the function that...

Question 14

Is the function graphed in the following figure invertible?

Accepted Answer

The answer of Is the function graphed in the following...

Question 15

A spherical cell takes in nutrients through its cell wall at a rate proportional to the area of the cell wall.The rate at which the cell uses nutrients is proportional to its volume.Which of the following expresses the rate at which the cell uses nutrients as a function of its radius, r.(A is a constant.)

Accepted Answer

A)  $\frac{A}{r^{2}}$ 
B)  $\frac{A}{r^{3}}$ 
C)  $A r^{2}$ 
D)  $A r^{3}$ 
A)  $\frac{A}{r^{2}}$ 
B)  $\frac{A}{r^{3}}$ 
C)  $A r^{2}$ 
D)  $A r^{3}$

Question 16

An exponentially decaying substance was weighed every hour and the results are given below.What is the approximate half-life, in hours, of the substance? Round to 1 decimal place.
 $\begin{array}{cc}
\text { Time } & \text { Weight (in grams } \
9 \mathrm{am} & 16 \
10 \mathrm{am} & 14.623 \
11 \mathrm{am} & 13.364 \
12 \text { noon } & 12.214 \
1 \mathrm{pm} & 11.163
\end{array}$

Accepted Answer

The answer of An exponentially decaying substance was weighed every...

Question 17

The data in the table describe the percentage of fissures that developed in turbines after h hours of running time.There is moderate linear relationship (r = 0.93)between the number of hours the turbines ran and the percentage of turbines that developed fissures.Which of the formulas below best models the linear relationship? $\begin{array}{cccc}
\text { Hours Run } & \begin{array}{c}
\text { Number of } \
\text { Turbines Run }
\end{array} & \begin{array}{c}
\text { Number of } \
\text { Fissures }
\end{array} & \begin{array}{c}
\% \text { of Turbine } \
\text { with Fissures }
\end{array} \
400 & 39 & 0 & 0 \
1000 & 53 & 4 & 0.08 \
1400 & 33 & 2 & 0.06 \
1800 & 73 & 7 & 0.1 \
2200 & 30 & 5 & 0.17 \
2600 & 39 & 9 & 0.23 \
3000 & 42 & 9 & 0.21 \
3400 & 13 & 6 & 0.46 \
3800 & 34 & 22 & 0.65 \
4200 & 40 & 21 & 0.53 \
4600 & 36 & 21 & 0.58
\end{array}$

Accepted Answer

A)  $f=0.00016 h-0.134$ 
B)  $f=1.6 h-0.133$ 
C)  $f=-0.002 h+0.132$ 
D)  $f=0.93 h-0.13$ 
A)  $f=0.00016 h-0.134$ 
B)  $f=1.6 h-0.133$ 
C)  $f=-0.002 h+0.132$ 
D)  $f=0.93 h-0.13$

Question 18

What is the period of the function $c(x)=\cos x+0.5 \cos 5 x$
 ?

Accepted Answer

A)  $2 \pi$ 
B)  $\pi$ 
C)  $\frac{\pi}{5}$ 
D) The function is not periodic 
A)  $2 \pi$ 
B)  $\pi$ 
C)  $\frac{\pi}{5}$ 
D) The function is not periodic

Question 19

A bar of soap starts out at 175 grams.What is the formula for the quantity S grams of soap remaining after t days if the decrease is 10 grams per day?

Accepted Answer

The answer of A bar of soap starts out at...

Question 20

Find a possible equation for the following function given a root at (0,0), a vertical asymptote at y=-1 and horizontal asymptote at x=2.

Accepted Answer

The answer of Find a possible equation for the following...

The curve W = f(t), given in the graph below, comes from the Wall Street Journal, September 4, 1992.W is a function.

Temperatures in Town A oscillate daily between 30° F at 4am and 60° F at 4pm.The temperature in Town B is consistently 10° F colder than in Town A.What does the formula $H=-15 \cos \left(\frac{\pi}{12} t\right)+45$ represent?

Graphically find a solution to the equation $6^{x}=x^{6}$ in the interval $[-1 \leq x \leq 1]$ .Give your answer accurate to 2 decimal places.

Is the function $\frac{1}{\sqrt{x^{2}-9}}$ continuous on the interval $0 \leq x \leq 4$ ?

The graph of a function y = f(x)is given below.Sketch a graph of it's inverse function on the same axes.

Suppose f(x)and g(x)are both increasing functions. a)Must f(g(x))be an increasing function? If so, explain why.If not, give an example. b)Must f(g(x))be invertible? If so explain why.If not, give an example.

On the $x-$ interval between E and F, the function graphed below is: Mark all that apply.

Given the graphs of $y=g(x)$ and $y=f(x)$ in the following figure, estimate g(f(5)).

Find $\lim _{x \rightarrow 0} \frac{1}{6 x^{2}}$ if it exists.

Given the function $y=f(x)=\frac{8}{5 x-8}$ , give a formula for the inverse function of f(x).

Find the equation for the line L shown below.

Write a formula representing the function that says: The circumference of a circle is proportional to the diameter of the circle.

Is the function graphed in the following figure invertible?

An exponentially decaying substance was weighed every hour and the results are given below.What is the approximate half-life, in hours, of the substance? Round to 1 decimal place. Time Weight (in grams 9 16 10 14.623 11 13.364 12 noon 12.214 1 11.163

What is the period of the function $c(x)=\cos x+0.5 \cos 5 x$ ?

A bar of soap starts out at 175 grams.What is the formula for the quantity S grams of soap remaining after t days if the decrease is 10 grams per day?

Find a possible equation for the following function given a root at (0,0), a vertical asymptote at y=-1 and horizontal asymptote at x=2.

Key Concept: the Derivative

Short-Cuts to Differentiation

Using the Derivative

Key Concept- the Definite Integral

Constructing Antiderivatives

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Exam 1: A Library of Functions

The curve W = f(t), given in the graph below, comes from the Wall Street Journal, September 4, 1992.W is a function.

Temperatures in Town A oscillate daily between 30° F at 4am and 60° F at 4pm.The temperature in Town B is consistently 10° F colder than in Town A.What does the formula H=−15cos⁡(π12t)+45H=-15 \cos \left(\frac{\pi}{12} t\right)+45H=−15cos(12π​t)+45 represent?

Graphically find a solution to the equation 6x=x66^{x}=x^{6}6x=x6 in the interval [−1≤x≤1][-1 \leq x \leq 1][−1≤x≤1] .Give your answer accurate to 2 decimal places.

Is the function 1x2−9\frac{1}{\sqrt{x^{2}-9}}x2−9​1​ continuous on the interval 0≤x≤40 \leq x \leq 40≤x≤4 ?

Use the following figure to give the approximate value (to the nearest integer)of lim⁡x→−4f(x)\lim _{x \rightarrow-4} f(x)limx→−4​f(x) .If the limit does not exist, enter "DNE".

The graph of a function y = f(x)is given below.Sketch a graph of it's inverse function on the same axes.

Suppose f(x)and g(x)are both increasing functions. a)Must f(g(x))be an increasing function? If so, explain why.If not, give an example. b)Must f(g(x))be invertible? If so explain why.If not, give an example.

On the x−x-x− interval between E and F, the function graphed below is: Mark all that apply.

Given the graphs of y=g(x)y=g(x)y=g(x) and y=f(x)y=f(x)y=f(x) in the following figure, estimate g(f(5)).

Find lim⁡x→016x2\lim _{x \rightarrow 0} \frac{1}{6 x^{2}}limx→0​6x21​ if it exists.

Given the function y=f(x)=85x−8y=f(x)=\frac{8}{5 x-8}y=f(x)=5x−88​ , give a formula for the inverse function of f(x).

Find the equation for the line L shown below.

Write a formula representing the function that says: The circumference of a circle is proportional to the diameter of the circle.

Is the function graphed in the following figure invertible?

An exponentially decaying substance was weighed every hour and the results are given below.What is the approximate half-life, in hours, of the substance? Round to 1 decimal place. Time Weight (in grams 9 16 10 14.623 11 13.364 12 noon 12.214 1 11.163

What is the period of the function c(x)=cos⁡x+0.5cos⁡5xc(x)=\cos x+0.5 \cos 5 xc(x)=cosx+0.5cos5x ?

A bar of soap starts out at 175 grams.What is the formula for the quantity S grams of soap remaining after t days if the decrease is 10 grams per day?

Find a possible equation for the following function given a root at (0,0), a vertical asymptote at y=-1 and horizontal asymptote at x=2.

Key Concept: the Derivative

Short-Cuts to Differentiation

Using the Derivative

Key Concept- the Definite Integral

Constructing Antiderivatives

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Temperatures in Town A oscillate daily between 30° F at 4am and 60° F at 4pm.The temperature in Town B is consistently 10° F colder than in Town A.What does the formula $H=-15 \cos \left(\frac{\pi}{12} t\right)+45$ represent?

Graphically find a solution to the equation $6^{x}=x^{6}$ in the interval $[-1 \leq x \leq 1]$ .Give your answer accurate to 2 decimal places.

Is the function $\frac{1}{\sqrt{x^{2}-9}}$ continuous on the interval $0 \leq x \leq 4$ ?

On the $x-$ interval between E and F, the function graphed below is: Mark all that apply.

Given the graphs of $y=g(x)$ and $y=f(x)$ in the following figure, estimate g(f(5)).

Find $\lim _{x \rightarrow 0} \frac{1}{6 x^{2}}$ if it exists.

Given the function $y=f(x)=\frac{8}{5 x-8}$ , give a formula for the inverse function of f(x).

What is the period of the function $c(x)=\cos x+0.5 \cos 5 x$ ?