Question 1

Solve the problem.
-At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $$C(x)=5.68 x+21,000$$
What is the marginal cost per item?

Accepted Answer

A)  $\$ 5.68$ 
B)  $\$ 20,994.32$ 
C)  $\$ 21,000$ 
D)  $\$ 21,005.68$ 
A)  $\$ 5.68$ 
B)  $\$ 20,994.32$ 
C)  $\$ 21,000$ 
D)  $\$ 21,005.68$

Question 2

Solve the problem.
-James owns a cafe. A mathematical model connecting $p$, the profit per day from selling coffee (in dollars) and $x$, the price per cup of coffee (in dollars) is $$p(x)=-x^{2}+30 x+36$$
Find the profit per day if the price per cup of coffee is $\$ 1.90$. Round to the nearest dollar.

Accepted Answer

A)  $\$ 245$ 
B)  $\$ 570$ 
C)  $\$ 317$ 
D)  $\$ 89$ 
A)  $\$ 245$ 
B)  $\$ 570$ 
C)  $\$ 317$ 
D)  $\$ 89$

Question 3

Evaluate the function.
-Given that $f(x)=\sqrt{5 x-6}$, and $f(p)$.

Accepted Answer

A)  $\sqrt{5 p-6}$ 
B)  $\sqrt{5 x-p}$ 
C)  $\sqrt{\mathrm{px}-6}$ 
D)  $5 p-6$ 
A)  $\sqrt{5 p-6}$ 
B)  $\sqrt{5 x-p}$ 
C)  $\sqrt{\mathrm{px}-6}$ 
D)  $5 p-6$

Question 4

Graph the function.
-$f(x)=x^{3}+4 x+1$

Accepted Answer

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

Question 5

Solve the problem.
-A rectangular garden is bounded on one side by a house and is to be fenced on the other three sides. Fencing material costs $\$ 12$ per foot for the side parallel to the house and $\$ 25$ per foot for the other two sides. What are the dimensions of the garden of largest possible area if $\$ 1800$ is to be spent for fencing material?

Accepted Answer

A)  $77 \mathrm{ft}$ by $17 \mathrm{ft}$ with the long side parallel to the house 
B)  $71 \mathrm{ft}$ by $20 \mathrm{ft}$ with the long side parallel to the house 
C)  $75 \mathrm{ft}$ by $18 \mathrm{ft}$ with the long side parallel to the house 
D)  $79 \mathrm{ft}$ by $16 \mathrm{ft}$ with the long side parallel to the house 
A)  $77 \mathrm{ft}$ by $17 \mathrm{ft}$ with the long side parallel to the house 
B)  $71 \mathrm{ft}$ by $20 \mathrm{ft}$ with the long side parallel to the house 
C)  $75 \mathrm{ft}$ by $18 \mathrm{ft}$ with the long side parallel to the house 
D)  $79 \mathrm{ft}$ by $16 \mathrm{ft}$ with the long side parallel to the house

Question 6

Graph the piecewise linear function.
-$f(x)= \begin{cases}5, & x \geq 1 \ -1-x, & x<1\end{cases}$

Accepted Answer

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

Question 7

Give the equation of the horizontal asymptote of the rational function.
-$h(x)=\frac{4 x^{2}-8 x-6}{9 x^{2}-3 x+3}$

Accepted Answer

A)  None 
B)  $\mathrm{y}=\frac{4}{9}$ 
C)  $\mathrm{y}=\frac{8}{3}$ 
D)  $y=0$ 
A)  None 
B)  $\mathrm{y}=\frac{4}{9}$ 
C)  $\mathrm{y}=\frac{8}{3}$ 
D)  $y=0$

Question 8

Solve the problem.
-If the average cost per unit $C(x)$ to produce $x$ units of plywood is given by $C(x)=\frac{1200}{x+40}$, what do 800 units cost? Round your answer to the nearest cent.

Accepted Answer

A)  $\$ 320.00$ 
B)  $\$ 24,000.00$ 
C)  $\$ 1142.86$ 
D)  $\$ 1199.95$ 
A)  $\$ 320.00$ 
B)  $\$ 24,000.00$ 
C)  $\$ 1142.86$ 
D)  $\$ 1199.95$

Question 9

Graph the rational function.
-$f(x)=-\frac{1}{x-4}$

Accepted Answer

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

Question 10

Evaluate the function.
-Find $f(k-1)$ when: $f(x)=3 x^{2}+3 x+3$

Accepted Answer

A)  $f(k-1)=-3 k^{2}+3 k+3$ 
B)  $f(k-1)=3 k^{2}+12 k+9$ 
C)  $f(k-1)=3 k^{2}-3 k+9$ 
D)  $f(k-1)=3 k^{2}-3 k+3$ 
A)  $f(k-1)=-3 k^{2}+3 k+3$ 
B)  $f(k-1)=3 k^{2}+12 k+9$ 
C)  $f(k-1)=3 k^{2}-3 k+9$ 
D)  $f(k-1)=3 k^{2}-3 k+3$

Question 11

State the domain of the given function.
-$f(x)=|8 x+4|$

Accepted Answer

A)  all real number except $-\frac{1}{2}$ 
B)  $[0, \infty)$ 
C)  $\left[-\frac{1}{2}, \infty\right)$ 
D)  $(-\infty, \infty)$ 
A)  all real number except $-\frac{1}{2}$ 
B)  $[0, \infty)$ 
C)  $\left[-\frac{1}{2}, \infty\right)$ 
D)  $(-\infty, \infty)$

Question 12

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point.
-vertex $(4,5)$; point $(6,9)$

Accepted Answer

A)  $P(x)=-x^{2}-8 x+5$ 
B)  $P(x)=x^{2}-4 x+5$ 
C)  $P(x)=x^{2}-8 x+21$ 
D)  $P(x)=6 x^{2}-8 x+21$ 
A)  $P(x)=-x^{2}-8 x+5$ 
B)  $P(x)=x^{2}-4 x+5$ 
C)  $P(x)=x^{2}-8 x+21$ 
D)  $P(x)=6 x^{2}-8 x+21$

Question 13

Solve the problem.
-A new car was purchased for $\$ 16,400$, and 4 years later it was worth $\$ 8800$. Assume that the depreciation in value is given by a linear equation. Find the value of the car at the end of 6 years.

Accepted Answer

A)  $\$ 12,600$ 
B)  $\$ 7600$ 
C)  $\$ 20,200$ 
D)  $\$ 5000$ 
A)  $\$ 12,600$ 
B)  $\$ 7600$ 
C)  $\$ 20,200$ 
D)  $\$ 5000$

Question 14

Solve the problem.
-A charter flight charges a fare of $\$ 300$ per person plus $\$ 5$ per person for each unsold seat on the plane. If the plane holds 228 passengers and if $x$ represents the number of unsold seats, an expression for the total revenue received for the flight is $R(x)=(228-x)(300+5 x)$. Determine the number of unsold seats that will produce the maximum revenue.

Accepted Answer

A)  79 
B)  84 
C)  89 
D)  168 
A)  79 
B)  84 
C)  89 
D)  168

Question 15

Solve the problem.
-If the price of a book is $p(x)=47-\frac{x}{10}$, then $x$ books will be sold. Find an expression for the total revenue from the sale of $x$ books.

Accepted Answer

A)  $R(x)=47-\frac{x}{10}$ 
B)  $R(x)=47 x-\frac{x}{10}$ 
C)  $R(x)=47-\frac{x}{10}+x$ 
D)  $R(x)=47 x-\frac{x^{2}}{10}$ 
A)  $R(x)=47-\frac{x}{10}$ 
B)  $R(x)=47 x-\frac{x}{10}$ 
C)  $R(x)=47-\frac{x}{10}+x$ 
D)  $R(x)=47 x-\frac{x^{2}}{10}$

Question 16

Solve the problem.
-Given the following revenue and cost functions, find the break-even point to the nearest tenth. (Recall that profit equals revenue minus cost.)
$$R(x)=59 x-2 x^{2} ; C(x)=25 x+96$$

Accepted Answer

A)  13.4 or 3.6 
B)  29.5 
C)  17.0 
D)  13.5 or 3.5 
A)  13.4 or 3.6 
B)  29.5 
C)  17.0 
D)  13.5 or 3.5

Question 17

For the given function, find $\frac{f(x+h)-f(x)}{h}$.
-$3 x^{2}+3$

Accepted Answer

A)  $6 x+3 h$ 
B)  $3 \mathrm{~h}$ 
C)  $\frac{6 x h+3 h^{2}+6}{h}$ 
D)  1 
A)  $6 x+3 h$ 
B)  $3 \mathrm{~h}$ 
C)  $\frac{6 x h+3 h^{2}+6}{h}$ 
D)  1

Question 18

Evaluate the function.
-Given that $f(x)=3-8 x$, find $f(-r)$.

Accepted Answer

A)  $3+8 r$ 
B)  $r-8 x$ 
C)  $3-8 r$ 
D)  $3+\mathrm{rx}$ 
A)  $3+8 r$ 
B)  $r-8 x$ 
C)  $3-8 r$ 
D)  $3+\mathrm{rx}$

Question 19

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)  no 
B)  yes; 4,6 
C)  yes; 3,5 
D)  yes; 4 only 
A)  no 
B)  yes; 4,6 
C)  yes; 3,5 
D)  yes; 4 only

Question 20

Solve the problem.
-At a manufacturing plant, the total cost (in dollars) to produce $x$ items is
$C(x)=2.75 x+3270$.
What is the average cost per item?

Accepted Answer

A)  $\$ 3270$ 
B)  $\$ 3272.75$ 
C)  $\frac{\$ 3270}{x}+\$ 2.75$ 
D)  $\$ 2.75$ 
A)  $\$ 3270$ 
B)  $\$ 3272.75$ 
C)  $\frac{\$ 3270}{x}+\$ 2.75$ 
D)  $\$ 2.75$

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=5.68 x+21,000$ What is the marginal cost per item?

Evaluate the function. -Given that $f(x)=\sqrt{5 x-6}$ , and $f(p)$ .

Graph the function. - $f(x)=x^{3}+4 x+1$ $Graph the function. - f(x)=x^{3}+4 x+1$

Graph the piecewise linear function. - $f(x)= \begin{cases}5, & x \geq 1 \\ -1-x, & x<1\end{cases}$ $Graph the piecewise linear function. - f(x)= \begin{cases}5, & x \geq 1 \\ -1-x, & x<1\end{cases}$

Give the equation of the horizontal asymptote of the rational function. - $h(x)=\frac{4 x^{2}-8 x-6}{9 x^{2}-3 x+3}$

Solve the problem. -If the average cost per unit $C(x)$ to produce $x$ units of plywood is given by $C(x)=\frac{1200}{x+40}$ , what do 800 units cost? Round your answer to the nearest cent.

Graph the rational function. - $f(x)=-\frac{1}{x-4}$ $Graph the rational function. - f(x)=-\frac{1}{x-4}$

Evaluate the function. -Find $f(k-1)$ when: $f(x)=3 x^{2}+3 x+3$

State the domain of the given function. - $f(x)=|8 x+4|$

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex $(4,5)$ ; point $(6,9)$

Solve the problem. -A new car was purchased for $\$ 16,400$ , and 4 years later it was worth $\$ 8800$ . Assume that the depreciation in value is given by a linear equation. Find the value of the car at the end of 6 years.

Solve the problem. -If the price of a book is $p(x)=47-\frac{x}{10}$ , then $x$ books will be sold. Find an expression for the total revenue from the sale of $x$ books.

Solve the problem. -Given the following revenue and cost functions, find the break-even point to the nearest tenth. (Recall that profit equals revenue minus cost.) $R(x)=59 x-2 x^{2} ; C(x)=25 x+96$

For the given function, find $\frac{f(x+h)-f(x)}{h}$ . - $3 x^{2}+3$

Evaluate the function. -Given that $f(x)=3-8 x$ , find $f(-r)$ .

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. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=2.75 x+3270$ . What is the average cost per item?

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

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce xxx items is C(x)=5.68x+21,000C(x)=5.68 x+21,000C(x)=5.68x+21,000 What is the marginal cost per item?

Evaluate the function. -Given that f(x)=5x−6f(x)=\sqrt{5 x-6}f(x)=5x−6​ , and f(p)f(p)f(p) .

Graph the function. - f(x)=x3+4x+1f(x)=x^{3}+4 x+1f(x)=x3+4x+1

Graph the piecewise linear function. - f(x)={5,x≥1−1−x,x<1f(x)= \begin{cases}5, & x \geq 1 \\ -1-x, & x<1\end{cases}f(x)={5,−1−x,​x≥1x<1​

Give the equation of the horizontal asymptote of the rational function. - h(x)=4x2−8x−69x2−3x+3h(x)=\frac{4 x^{2}-8 x-6}{9 x^{2}-3 x+3}h(x)=9x2−3x+34x2−8x−6​

Solve the problem. -If the average cost per unit C(x)C(x)C(x) to produce xxx units of plywood is given by C(x)=1200x+40C(x)=\frac{1200}{x+40}C(x)=x+401200​ , what do 800 units cost? Round your answer to the nearest cent.

Graph the rational function. - f(x)=−1x−4f(x)=-\frac{1}{x-4}f(x)=−x−41​

Evaluate the function. -Find f(k−1)f(k-1)f(k−1) when: f(x)=3x2+3x+3f(x)=3 x^{2}+3 x+3f(x)=3x2+3x+3

State the domain of the given function. - f(x)=∣8x+4∣f(x)=|8 x+4|f(x)=∣8x+4∣

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex (4,5)(4,5)(4,5) ; point (6,9)(6,9)(6,9)

Solve the problem. -A new car was purchased for $16,400\$ 16,400$16,400 , and 4 years later it was worth $8800\$ 8800$8800 . Assume that the depreciation in value is given by a linear equation. Find the value of the car at the end of 6 years.

Solve the problem. -If the price of a book is p(x)=47−x10p(x)=47-\frac{x}{10}p(x)=47−10x​ , then xxx books will be sold. Find an expression for the total revenue from the sale of xxx books.

Solve the problem. -Given the following revenue and cost functions, find the break-even point to the nearest tenth. (Recall that profit equals revenue minus cost.) R(x)=59x−2x2;C(x)=25x+96R(x)=59 x-2 x^{2} ; C(x)=25 x+96R(x)=59x−2x2;C(x)=25x+96

For the given function, find f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ . - 3x2+33 x^{2}+33x2+3

Evaluate the function. -Given that f(x)=3−8xf(x)=3-8 xf(x)=3−8x , find f(−r)f(-r)f(−r) .

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. -At a manufacturing plant, the total cost (in dollars) to produce xxx items is C(x)=2.75x+3270C(x)=2.75 x+3270C(x)=2.75x+3270 . What is the average cost per item?

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

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=5.68 x+21,000$ What is the marginal cost per item?

Evaluate the function. -Given that $f(x)=\sqrt{5 x-6}$ , and $f(p)$ .

Graph the function. - $f(x)=x^{3}+4 x+1$ $Graph the function. - f(x)=x^{3}+4 x+1$

Graph the piecewise linear function. - $f(x)= \begin{cases}5, & x \geq 1 \\ -1-x, & x<1\end{cases}$ $Graph the piecewise linear function. - f(x)= \begin{cases}5, & x \geq 1 \\ -1-x, & x<1\end{cases}$

Give the equation of the horizontal asymptote of the rational function. - $h(x)=\frac{4 x^{2}-8 x-6}{9 x^{2}-3 x+3}$

Solve the problem. -If the average cost per unit $C(x)$ to produce $x$ units of plywood is given by $C(x)=\frac{1200}{x+40}$ , what do 800 units cost? Round your answer to the nearest cent.

Graph the rational function. - $f(x)=-\frac{1}{x-4}$ $Graph the rational function. - f(x)=-\frac{1}{x-4}$

Evaluate the function. -Find $f(k-1)$ when: $f(x)=3 x^{2}+3 x+3$

State the domain of the given function. - $f(x)=|8 x+4|$

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex $(4,5)$ ; point $(6,9)$

Solve the problem. -A new car was purchased for $\$ 16,400$ , and 4 years later it was worth $\$ 8800$ . Assume that the depreciation in value is given by a linear equation. Find the value of the car at the end of 6 years.

Solve the problem. -If the price of a book is $p(x)=47-\frac{x}{10}$ , then $x$ books will be sold. Find an expression for the total revenue from the sale of $x$ books.

Solve the problem. -Given the following revenue and cost functions, find the break-even point to the nearest tenth. (Recall that profit equals revenue minus cost.) $R(x)=59 x-2 x^{2} ; C(x)=25 x+96$

For the given function, find $\frac{f(x+h)-f(x)}{h}$ . - $3 x^{2}+3$

Evaluate the function. -Given that $f(x)=3-8 x$ , find $f(-r)$ .

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=2.75 x+3270$ . What is the average cost per item?