Question 1

Determine whether the following rule defines $y$ as a function of $x$.
-$y=|x-3|$

Accepted Answer

A) True 
 B)False  True

Question 2

Solve the problem.
-The manager of a CD store has found that if the price of a CD is $p(x)=90-\frac{x}{8}$, then $x C D$ will be sold. Find an expression for the total revenue from the sale of $x$ CDs
(hint: revenue $=$ demand $\times$ price). Use your expression to determine the maximum revenue.

Accepted Answer

A)  $\$ 32,400$ 
B)  $\$ 8100$ 
C)  $\$ 64,800$ 
D)  $\$ 16,200$ 
A)  $\$ 32,400$ 
B)  $\$ 8100$ 
C)  $\$ 64,800$ 
D)  $\$ 16,200$ D

Question 3

Graph the parabola.
-$y=5 x^{2}+3$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)    D

Question 4

Solve the problem.
-Regrind, Inc. regrinds used typewriter platens. The cost per platen is $\$ 1.50$. The fixed cost to run the grinding machine is $\$ 232$ per day. If the company sells the reground platens for $\$ 5.50$, how many must be reground daily to reach the break-even point?

Accepted Answer

A) 33 platens 
B)  154 platens 
C)  38 platens 
D)  58 platens 
A) 33 platens 
B)  154 platens 
C)  38 platens 
D)  58 platens

Question 5

Find the appropriate linear cost or revenue function.
-Find the revenue function given the following information. Fixed cost: $\$ 840$; marginal cost per item: $\$ 10$; item sells for $\$ 36$

Accepted Answer

A)  $R(x)=10 x$ 
B)  $R(x)=26 x-840$ 
C)  $R(x)=36 x$ 
D)  $R(x)=26 x$ 
A)  $R(x)=10 x$ 
B)  $R(x)=26 x-840$ 
C)  $R(x)=36 x$ 
D)  $R(x)=26 x$

Question 6

Solve the problem.
-Suppose the supply and demand for a certain videotape are given by:
$$\text { supply: } \mathrm{p}=\frac{1}{5} \mathrm{q}^{2} ; \quad \text { demand: } \mathrm{p}=-\frac{1}{5} \mathrm{q}^{2}+36$$
Where $p$ is price and $q$ is quantity.
Find the equilibrium demand.

Accepted Answer

A)  About 8 
B)  About 11 
C)  About 9 
D)  About 10 
A)  About 8 
B)  About 11 
C)  About 9 
D)  About 10

Question 7

Solve the problem.
-A ball is thrown vertically upward at an initial speed of $40 \mathrm{ft} / \mathrm{sec}$. Its height (in feet) after $t$ seconds is given by
$$h(t)=t(40-16 t)$$
After how many seconds does the ball reach its maximum height?

Accepted Answer

A)  1.25 seconds 
B)  1.67 seconds 
C)  2.5 seconds 
D)  5 seconds 
A)  1.25 seconds 
B)  1.67 seconds 
C)  2.5 seconds 
D)  5 seconds

Question 8

Graph the function.
-$f(x)=|x|-1$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

State the domain of the given function.
-$f(x)=\frac{1}{x+6}$

Accepted Answer

A)  all real numbers except 6 
B)  all real numbers except -6 
C)  $(-6, \infty)$ 
D)  $(-\infty, \infty)$ 
A)  all real numbers except 6 
B)  all real numbers except -6 
C)  $(-6, \infty)$ 
D)  $(-\infty, \infty)$

Question 10

Solve the problem.
-The demand for a certain type of modem is given by
$$p=480-x$$
Where $\mathrm{p}$ is the price when $\mathrm{x}$ units are demanded. Determine the price that will produce the maximum revenue. (Hint: First find the revenue $R(x)$, that would be obtained at a demand of $x$ ).

Accepted Answer

A)  $\$ 260$ 
B)  $\$ 240$ 
C)  $\$ 48$ 
D)  $\$ 480$ 
A)  $\$ 260$ 
B)  $\$ 240$ 
C)  $\$ 48$ 
D)  $\$ 480$

Question 11

Solve the problem.
-Suppose a car rental company charges $\$ 74$ for the first day and $\$ 24$ for each additional or partial day. Let $S(x)$ represent the cost of renting a car for $x$ days. Find the value of $S(3.5)$.

Accepted Answer

A)  $\$ 158$ 
B)  $\$ 146$ 
C)  $\$ 84$ 
D)  $\$ 134$ 
A)  $\$ 158$ 
B)  $\$ 146$ 
C)  $\$ 84$ 
D)  $\$ 134$

Question 12

Graph the piecewise linear function.
-$f(x)= \begin{cases}1, & x \geq-1 \ x-3, & x<-1\end{cases}$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Find a quadratic function that models the data.
-The table shows the population of a city in selected years. Data are in thousands rounded to the nearest hundred.
 
Let $\mathrm{x}=0$ correspond to 1970 and let $\mathrm{f}(\mathrm{x})$ be the population of the city (in thousands) in year $\mathrm{x}$. Using the point $(0,77.9)$ as the vertex and and the data from 1995, determine a quadratic function $f(x)=a(x-h)^{2}+k$ that models the data.

Accepted Answer

A)  $f(x)=1.58 x^{2}+77.9$ 
B)  $f(x)=0.079 x^{2}+77.9$ 
C)  $f(x)=0.0632 x^{2}+77.9$ 
D)  $f(x)=0.31248 x^{2}-77.9$ 
A)  $f(x)=1.58 x^{2}+77.9$ 
B)  $f(x)=0.079 x^{2}+77.9$ 
C)  $f(x)=0.0632 x^{2}+77.9$ 
D)  $f(x)=0.31248 x^{2}-77.9$

Question 14

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point.
-vertex $(4,4)$; point $(2,8)$

Accepted Answer

A)  $P(x)=2 x^{2}-8 x-20$ 
B)  $P(x)=x^{2}-4 x+4$ 
C)  $P(x)=x^{2}-8 x+20$ 
D)  $P(x)=-x^{2}-8 x+4$ 
A)  $P(x)=2 x^{2}-8 x-20$ 
B)  $P(x)=x^{2}-4 x+4$ 
C)  $P(x)=x^{2}-8 x+20$ 
D)  $P(x)=-x^{2}-8 x+4$

Question 15

Solve the problem.
-The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

Accepted Answer

A)  yes; 5 only 
B)  yes; 4 only 
C)  yes; 3,5 
D)  yes; 3 only 
A)  yes; 5 only 
B)  yes; 4 only 
C)  yes; 3,5 
D)  yes; 3 only

Question 16

Solve the problem.
-The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$.

Accepted Answer

A)  yes; 4,6 
B)  yes; 4 only 
C)  no 
D)  yes; 6 only 
A)  yes; 4,6 
B)  yes; 4 only 
C)  no 
D)  yes; 6 only

Question 17

Graph the linear function.
-$f(x)=\frac{1}{6} x+1$

Accepted Answer

A)    
B)    
A)    
B)

Question 18

Use the vertical line test to determine if the graph is a graph of a function.
-

Accepted Answer

A) True 
 B)False

Question 19

Give the equation of the horizontal asymptote of the rational function.
-$g(x)=\frac{x-3}{x-4}$

Accepted Answer

A)  $x=4$ 
B)  $y=1$ 
C)  $y=0$ 
D)  $\mathrm{y}=\frac{3}{4}$ 
A)  $x=4$ 
B)  $y=1$ 
C)  $y=0$ 
D)  $\mathrm{y}=\frac{3}{4}$

Question 20

Solve the problem.
-The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$.

Accepted Answer

A)  yes; 5,6 
B)  yes; none 
C)  yes; 6 only 
D)  yes; 5 only 
A)  yes; 5,6 
B)  yes; none 
C)  yes; 6 only 
D)  yes; 5 only

Determine whether the following rule defines $y$ as a function of $x$ . - $y=|x-3|$

Solve the problem. -The manager of a CD store has found that if the price of a CD is $p(x)=90-\frac{x}{8}$ , then $x C D$ will be sold. Find an expression for the total revenue from the sale of $x$ CDs (hint: revenue $=$ demand $\times$ price). Use your expression to determine the maximum revenue.

Graph the parabola. - $y=5 x^{2}+3$ $Graph the parabola. - y=5 x^{2}+3$

Solve the problem. -Regrind, Inc. regrinds used typewriter platens. The cost per platen is $\$ 1.50$ . The fixed cost to run the grinding machine is $\$ 232$ per day. If the company sells the reground platens for $\$ 5.50$ , how many must be reground daily to reach the break-even point?

Find the appropriate linear cost or revenue function. -Find the revenue function given the following information. Fixed cost: $\$ 840$ ; marginal cost per item: $\$ 10$ ; item sells for $\$ 36$

Solve the problem. -Suppose the supply and demand for a certain videotape are given by: $\text { supply: } \mathrm{p}=\frac{1}{5} \mathrm{q}^{2} ; \quad \text { demand: } \mathrm{p}=-\frac{1}{5} \mathrm{q}^{2}+36$ Where $p$ is price and $q$ is quantity. Find the equilibrium demand.

Solve the problem. -A ball is thrown vertically upward at an initial speed of $40 \mathrm{ft} / \mathrm{sec}$ . Its height (in feet) after $t$ seconds is given by $h(t)=t(40-16 t)$ After how many seconds does the ball reach its maximum height?

Graph the function. - $f(x)=|x|-1$

State the domain of the given function. - $f(x)=\frac{1}{x+6}$

Solve the problem. -The demand for a certain type of modem is given by $p=480-x$ Where $\mathrm{p}$ is the price when $\mathrm{x}$ units are demanded. Determine the price that will produce the maximum revenue. (Hint: First find the revenue $R(x)$ , that would be obtained at a demand of $x$ ).

Solve the problem. -Suppose a car rental company charges $\$ 74$ for the first day and $\$ 24$ for each additional or partial day. Let $S(x)$ represent the cost of renting a car for $x$ days. Find the value of $S(3.5)$ .

Graph the piecewise linear function. - $f(x)= \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}$ $Graph the piecewise linear function. - f(x)= \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}$

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex $(4,4)$ ; point $(2,8)$

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$ .

Graph the linear function. - $f(x)=\frac{1}{6} x+1$ $Graph the linear function. - f(x)=\frac{1}{6} x+1$

Use the vertical line test to determine if the graph is a graph of a function. -

Give the equation of the horizontal asymptote of the rational function. - $g(x)=\frac{x-3}{x-4}$

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$ .

Algebra and Equations

Graphs, Lines, and Inequalities

Exponential and Logarithmic Functions

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Exam 3: Functions and Graphs

Determine whether the following rule defines yyy as a function of xxx . - y=∣x−3∣y=|x-3|y=∣x−3∣

Graph the parabola. - y=5x2+3y=5 x^{2}+3y=5x2+3

Find the appropriate linear cost or revenue function. -Find the revenue function given the following information. Fixed cost: $840\$ 840$840 ; marginal cost per item: $10\$ 10$10 ; item sells for $36\$ 36$36

Solve the problem. -A ball is thrown vertically upward at an initial speed of 40ft/sec40 \mathrm{ft} / \mathrm{sec}40ft/sec . Its height (in feet) after ttt seconds is given by h(t)=t(40−16t)h(t)=t(40-16 t)h(t)=t(40−16t) After how many seconds does the ball reach its maximum height?

Graph the function. - f(x)=∣x∣−1f(x)=|x|-1f(x)=∣x∣−1

State the domain of the given function. - f(x)=1x+6f(x)=\frac{1}{x+6}f(x)=x+61​

Solve the problem. -Suppose a car rental company charges $74\$ 74$74 for the first day and $24\$ 24$24 for each additional or partial day. Let S(x)S(x)S(x) represent the cost of renting a car for xxx days. Find the value of S(3.5)S(3.5)S(3.5) .

Graph the piecewise linear function. - f(x)={1,x≥−1x−3,x<−1f(x)= \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}f(x)={1,x−3,​x≥−1x<−1​

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex (4,4)(4,4)(4,4) ; point (2,8)(2,8)(2,8)

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3,4,5,63,4,5,63,4,5,6 .

Graph the linear function. - f(x)=16x+1f(x)=\frac{1}{6} x+1f(x)=61​x+1

Use the vertical line test to determine if the graph is a graph of a function. -

Give the equation of the horizontal asymptote of the rational function. - g(x)=x−3x−4g(x)=\frac{x-3}{x-4}g(x)=x−4x−3​

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3,4,5,63,4,5,63,4,5,6 .

Algebra and Equations

Graphs, Lines, and Inequalities

Exponential and Logarithmic Functions

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Determine whether the following rule defines $y$ as a function of $x$ . - $y=|x-3|$

Graph the parabola. - $y=5 x^{2}+3$ $Graph the parabola. - y=5 x^{2}+3$

Find the appropriate linear cost or revenue function. -Find the revenue function given the following information. Fixed cost: $\$ 840$ ; marginal cost per item: $\$ 10$ ; item sells for $\$ 36$

Solve the problem. -A ball is thrown vertically upward at an initial speed of $40 \mathrm{ft} / \mathrm{sec}$ . Its height (in feet) after $t$ seconds is given by $h(t)=t(40-16 t)$ After how many seconds does the ball reach its maximum height?

Graph the function. - $f(x)=|x|-1$

State the domain of the given function. - $f(x)=\frac{1}{x+6}$

Solve the problem. -Suppose a car rental company charges $\$ 74$ for the first day and $\$ 24$ for each additional or partial day. Let $S(x)$ represent the cost of renting a car for $x$ days. Find the value of $S(3.5)$ .

Graph the piecewise linear function. - $f(x)= \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}$ $Graph the piecewise linear function. - f(x)= \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}$

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex $(4,4)$ ; point $(2,8)$

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$ .

Graph the linear function. - $f(x)=\frac{1}{6} x+1$ $Graph the linear function. - f(x)=\frac{1}{6} x+1$

Give the equation of the horizontal asymptote of the rational function. - $g(x)=\frac{x-3}{x-4}$

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$ .