Question 1

What are the upper and lower bounds for the function  f(x)=cos x-1  ?

Accepted Answer

The answer of What are the upper and lower bounds...

Question 2

Describe how the graph of $y=(5 x-5)^{2}$ can be obtained from the graph of $y=x^{2} .$

Accepted Answer

The answer of Describe how the graph of $y=(5 x-5)^{2}$...

Question 3

Give an example of a discontinuous function and state
why it is discontinuous.

Accepted Answer

The answer of Give an example of a discontinuous function...

Question 4

Find the domain of the function $f(x)=x^{2}+\sqrt{x-5}$ Give your answer in interval notation.

Accepted Answer

The answer of Find the domain of the function $f(x)=x^{2}+\sqrt{x-5}$...

Question 5

Five of the twelve basic functions are odd functions. Which are they?

Accepted Answer

The answer of Five of the twelve basic functions are...

Question 6

What are the upper and lower bounds for the function $ f(x)=\sin x+2 ? $

Accepted Answer

The answer of What are the upper and lower bounds...

Question 7

Solve $100 x^{2}+13 x=828$
by using the quadratic formula. Give your answer to one decimal place.

Accepted Answer

The answer of Solve $100 x^{2}+13 x=828$
by using the quadratic...

Question 8

Juan drives in city traffic for 2 hours. He travels 62 miles during that time. He averages 26 miles per hour less on this drive than he does on a country highway. What is his average speed on the country highway?

Accepted Answer

The answer of Juan drives in city traffic for 2...

Question 9

A rectangular field is to be enclosed by a fence. An
existing fence will form one side of the enclosure. The
amount of new fence bought for the other three sides is
1200 feet. What is the maximum area of the enclosed
field?
formula. Give your answer to one decimal place.

Accepted Answer

The answer of A rectangular field is to be enclosed...

Question 10

Use a graphing calculator to determine all local maxima and/or minima for the function $y=2 x^{3}-7 x^{2}-4 x$ Give the values where the extremum occur to two decimal places.

Accepted Answer

The answer of Use a graphing calculator to determine all...

Question 11

Graph the relation defined by the parametric equations below. Use an appropriate window size for $ -3 t 3 $.
$x=5-2 t^{2}, y=2(t-1)$

Accepted Answer

The answer of Graph the relation defined by the parametric...

Question 12

A cylindrical tank with diameter $ 30 \mathrm{ft} $ is filled with gasoline to a depth of $ 60 \mathrm{ft} $. The gasoline begins draining at a constant rate of 5 cubic feet per second. Write the volume of gasoline remaining in the tank $ t $ seconds after the tank begins draining as a function of $ t $.

Accepted Answer

The answer of A cylindrical tank with diameter \( 30...

Question 13

Let $f(x)=\sqrt{2-x}$
(a) Why does $f$ have an inverse that is a function?
(b) Find a rule for $f^{-1}(x)$ and state its domain.

Accepted Answer

The answer of Let $f(x)=\sqrt{2-x}$
(a) Why does $f$ have an...

Question 14

Find all vertical and horizontal asymptotes of the graph of 
$y=\frac{5 x}{2 x^{2}-11 x-6}$

Accepted Answer

The answer of Find all vertical and horizontal asymptotes of...

Question 15

Solve $\sqrt{x+2}=x-4$ algebraically and support graphically. Identify all extraneous solutions.

Accepted Answer

The answer of Solve $\sqrt{x+2}=x-4$ algebraically and support graphically. Identify...

Question 16

A cylindrical tank with diameter 25 meters is filled with gasoline to a depth of 40 meters. The gasoline begins draining at a constant rate of 4 cubic meters per second. Write the volume of gasoline remaining in the tank  t  seconds after the tank begins draining as a function of  t .

Accepted Answer

The answer of A cylindrical tank with diameter 25 meters...

Question 17

Solve the equation $-x^{2}-3 x+10=0$ Give exact answers.

Accepted Answer

The answer of Solve the equation $-x^{2}-3 x+10=0$ Give exact...

Question 18

Write an equation that models the following and solve.
How many gallons of vanilla ice cream with 12%
butterfat must be mixed with 20 gallons of chocolate ice
cream with 20% butterfat to make vanilla fudge ice
cream with 15% butterfat?

Accepted Answer

The answer of Write an equation that models the following...

Question 19

Suppose the point (3, -5) lies on a graph of an even
function. Determine a second point on the graph.

Accepted Answer

The answer of Suppose the point (3, -5) lies on...

Question 20

Let A represent the amount of money Paul has in his  pocket. Paul and his girl friend go out to dinner. They  spend x dollars on food, pay 8% tax on the dinner  check, and leave a 15% tip (not including the tax).
(a) Write a function relating the amount of money in  Paul's pocket to the amount they spend on food for dinner.
(b) If Paul has $46 in his pocket, what is the maximum  amount they could spend on food for dinner?

Accepted Answer

The answer of Let A represent the amount of money...

Exam 1: Functions and Graphs

What are the upper and lower bounds for the function f(x)=cos x-1 ?

Describe how the graph of $y=(5 x-5)^{2}$ can be obtained from the graph of $y=x^{2} .$

Give an example of a discontinuous function and state why it is discontinuous.

Find the domain of the function $f(x)=x^{2}+\sqrt{x-5}$ Give your answer in interval notation.

Five of the twelve basic functions are odd functions. Which are they?

What are the upper and lower bounds for the function $f(x)=\sin x+2 ?$

Solve $100 x^{2}+13 x=828$ by using the quadratic formula. Give your answer to one decimal place.

Juan drives in city traffic for 2 hours. He travels 62 miles during that time. He averages 26 miles per hour less on this drive than he does on a country highway. What is his average speed on the country highway?

A rectangular field is to be enclosed by a fence. An existing fence will form one side of the enclosure. The amount of new fence bought for the other three sides is 1200 feet. What is the maximum area of the enclosed field? formula. Give your answer to one decimal place.

Use a graphing calculator to determine all local maxima and/or minima for the function $y=2 x^{3}-7 x^{2}-4 x$ Give the values where the extremum occur to two decimal places.

Graph the relation defined by the parametric equations below. Use an appropriate window size for $-3 t 3$ . $x=5-2 t^{2}, y=2(t-1)$ $Graph the relation defined by the parametric equations below. Use an appropriate window size for -3 t 3 . x=5-2 t^{2}, y=2(t-1)$

A cylindrical tank with diameter $30 \mathrm{ft}$ is filled with gasoline to a depth of $60 \mathrm{ft}$ . The gasoline begins draining at a constant rate of 5 cubic feet per second. Write the volume of gasoline remaining in the tank $t$ seconds after the tank begins draining as a function of $t$ .

Let $f(x)=\sqrt{2-x}$ (a) Why does $f$ have an inverse that is a function? (b) Find a rule for $f^{-1}(x)$ and state its domain.

Find all vertical and horizontal asymptotes of the graph of $y=\frac{5 x}{2 x^{2}-11 x-6}$

Solve $\sqrt{x+2}=x-4$ algebraically and support graphically. Identify all extraneous solutions.

A cylindrical tank with diameter 25 meters is filled with gasoline to a depth of 40 meters. The gasoline begins draining at a constant rate of 4 cubic meters per second. Write the volume of gasoline remaining in the tank t seconds after the tank begins draining as a function of t .

Solve the equation $-x^{2}-3 x+10=0$ Give exact answers.

Write an equation that models the following and solve. How many gallons of vanilla ice cream with 12% butterfat must be mixed with 20 gallons of chocolate ice cream with 20% butterfat to make vanilla fudge ice cream with 15% butterfat?

Suppose the point (3, -5) lies on a graph of an even function. Determine a second point on the graph.

Exam 1: Functions and Graphs

What are the upper and lower bounds for the function f(x)=cos x-1 ?

Describe how the graph of y=(5x−5)2y=(5 x-5)^{2}y=(5x−5)2 can be obtained from the graph of y=x2.y=x^{2} .y=x2.

Give an example of a discontinuous function and state why it is discontinuous.

Find the domain of the function f(x)=x2+x−5f(x)=x^{2}+\sqrt{x-5}f(x)=x2+x−5​ Give your answer in interval notation.

Five of the twelve basic functions are odd functions. Which are they?

What are the upper and lower bounds for the function f(x)=sin⁡x+2? f(x)=\sin x+2 ? f(x)=sinx+2?

Solve 100x2+13x=828100 x^{2}+13 x=828100x2+13x=828 by using the quadratic formula. Give your answer to one decimal place.

Juan drives in city traffic for 2 hours. He travels 62 miles during that time. He averages 26 miles per hour less on this drive than he does on a country highway. What is his average speed on the country highway?

A rectangular field is to be enclosed by a fence. An existing fence will form one side of the enclosure. The amount of new fence bought for the other three sides is 1200 feet. What is the maximum area of the enclosed field? formula. Give your answer to one decimal place.

Use a graphing calculator to determine all local maxima and/or minima for the function y=2x3−7x2−4xy=2 x^{3}-7 x^{2}-4 xy=2x3−7x2−4x Give the values where the extremum occur to two decimal places.

Graph the relation defined by the parametric equations below. Use an appropriate window size for −3t3 -3 t 3 −3t3 . x=5−2t2,y=2(t−1)x=5-2 t^{2}, y=2(t-1)x=5−2t2,y=2(t−1)

Let f(x)=2−xf(x)=\sqrt{2-x}f(x)=2−x​ (a) Why does fff have an inverse that is a function? (b) Find a rule for f−1(x)f^{-1}(x)f−1(x) and state its domain.

Find all vertical and horizontal asymptotes of the graph of y=5x2x2−11x−6y=\frac{5 x}{2 x^{2}-11 x-6}y=2x2−11x−65x​

Solve x+2=x−4\sqrt{x+2}=x-4x+2​=x−4 algebraically and support graphically. Identify all extraneous solutions.

A cylindrical tank with diameter 25 meters is filled with gasoline to a depth of 40 meters. The gasoline begins draining at a constant rate of 4 cubic meters per second. Write the volume of gasoline remaining in the tank t seconds after the tank begins draining as a function of t .

Solve the equation −x2−3x+10=0-x^{2}-3 x+10=0−x2−3x+10=0 Give exact answers.

Write an equation that models the following and solve. How many gallons of vanilla ice cream with 12% butterfat must be mixed with 20 gallons of chocolate ice cream with 20% butterfat to make vanilla fudge ice cream with 15% butterfat?

Suppose the point (3, -5) lies on a graph of an even function. Determine a second point on the graph.

Describe how the graph of $y=(5 x-5)^{2}$ can be obtained from the graph of $y=x^{2} .$

Find the domain of the function $f(x)=x^{2}+\sqrt{x-5}$ Give your answer in interval notation.

What are the upper and lower bounds for the function $f(x)=\sin x+2 ?$

Solve $100 x^{2}+13 x=828$ by using the quadratic formula. Give your answer to one decimal place.

Use a graphing calculator to determine all local maxima and/or minima for the function $y=2 x^{3}-7 x^{2}-4 x$ Give the values where the extremum occur to two decimal places.

Graph the relation defined by the parametric equations below. Use an appropriate window size for $-3 t 3$ . $x=5-2 t^{2}, y=2(t-1)$ $Graph the relation defined by the parametric equations below. Use an appropriate window size for -3 t 3 . x=5-2 t^{2}, y=2(t-1)$

Let $f(x)=\sqrt{2-x}$ (a) Why does $f$ have an inverse that is a function? (b) Find a rule for $f^{-1}(x)$ and state its domain.

Find all vertical and horizontal asymptotes of the graph of $y=\frac{5 x}{2 x^{2}-11 x-6}$

Solve $\sqrt{x+2}=x-4$ algebraically and support graphically. Identify all extraneous solutions.

Solve the equation $-x^{2}-3 x+10=0$ Give exact answers.