Question 1

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

(a) $ A=1.23 x $
(b) $ 37.40 $

Question 2

Find the inverse relation of $f(x)=\frac{6 x+5}{3 x-1}$

Accepted Answer

$f^{-1}(x)=\frac{x+5}{3 x-6}$

Question 3

The graph of which of the following functions is bounded above by x=2?

Accepted Answer

C

Question 4

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 5

Write the equation whose graph can be obtained from the graph of $y=x^{2}$ by a vertical stretching of factor 4 , a reflection through the  x -axis, and a vertical shift 5 units up.

Accepted Answer

The answer of Write the equation whose graph can be...

Question 6

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 7

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 8

Alfred receives a salary of $2500 per month, and he
pays $550 per month in rent. What percentage of his
salary is spent on rent?

Accepted Answer

The answer of Alfred receives a salary of $2500 per...

Question 9

Let $f(x)=2 x^{3}-3 x^{2}+5 x+6$
Find an equation for g , the reflection of  f  across the  y -axis.

Accepted Answer

The answer of Let $f(x)=2 x^{3}-3 x^{2}+5 x+6$
Find an equation...

Question 10

Find the range of the function $f(x)=x^{3}+\sqrt{x-2}$ Give your answer in interval notation.

Accepted Answer

The answer of Find the range of the function $f(x)=x^{3}+\sqrt{x-2}$...

Question 11

Which of these functions is one-to-one?

Accepted Answer

Function B, $f(x)=6x +14$, is one-to-one because it is a linear function with a non-zero slope, which means it passes the horizontal line test. Linear functions with non-zero slopes are always one-to-one because each x-value maps to exactly one y-value, and each y-value is mapped from exactly one x-value.

Question 12

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 13

-The graph above is a slight variation of one of the ten basic functions. Which of the following equations best represents the graph?

Accepted Answer

The answer of 
-The graph above is a slight variation...

Question 14

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 15

Graph the relation defined by the parametric equations $ x=2 t^{2}-4 $ and $ y=2 t $. Use a $ [-5,5] $ by $ [-5,5] $ viewing window and $ -2 t 2 $.

Accepted Answer

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

Question 16

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 17

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 18

What two functions implicitly define the relation $x+|y|=2 ?$ What is the domain?

Accepted Answer

The answer of What two functions implicitly define the relation...

Question 19

(a) Find all the zeroes for the function $f(x)=3 x^{4}-6 x^{2}$
(b) List the intervals where the function $f(x)=3 x^{4}-6 x^{2}$ is increasing.

Accepted Answer

The answer of (a) Find all the zeroes for the...

Question 20

Describe how the graph of $f(x)=x^{4}-2$ can be transformed to the graph of $g(x)=(2 x)^{4}-2$

Accepted Answer

The answer of Describe how the graph of $f(x)=x^{4}-2$ can...

Quiz 1: Functions and Graphs

Find the inverse relation of $f(x)=\frac{6 x+5}{3 x-1}$

The graph of which of the following functions is bounded above by x=2?

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

Write the equation whose graph can be obtained from the graph of $y=x^{2}$ by a vertical stretching of factor 4 , a reflection through the x -axis, and a vertical shift 5 units up.

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

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.

Alfred receives a salary of $2500 per month, and he pays $550 per month in rent. What percentage of his salary is spent on rent?

Let $f(x)=2 x^{3}-3 x^{2}+5 x+6$ Find an equation for g , the reflection of f across the y -axis.

Find the range of the function $f(x)=x^{3}+\sqrt{x-2}$ Give your answer in interval notation.

Which of these functions is one-to-one?

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

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?

Graph the relation defined by the parametric equations $x=2 t^{2}-4$ and $y=2 t$ . Use a $[-5,5]$ by $[-5,5]$ viewing window and $-2 t 2$ . $Graph the relation defined by the parametric equations x=2 t^{2}-4 and y=2 t . Use a [-5,5] by [-5,5] viewing window and -2 t 2 .$

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

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

What two functions implicitly define the relation $x+|y|=2 ?$ What is the domain?

(a) Find all the zeroes for the function $f(x)=3 x^{4}-6 x^{2}$ (b) List the intervals where the function $f(x)=3 x^{4}-6 x^{2}$ is increasing.

Describe how the graph of $f(x)=x^{4}-2$ can be transformed to the graph of $g(x)=(2 x)^{4}-2$

Quiz 1: Functions and Graphs

Find the inverse relation of f(x)=6x+53x−1f(x)=\frac{6 x+5}{3 x-1}f(x)=3x−16x+5​

The graph of which of the following functions is bounded above by x=2?

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

Write the equation whose graph can be obtained from the graph of y=x2y=x^{2}y=x2 by a vertical stretching of factor 4 , a reflection through the x -axis, and a vertical shift 5 units up.

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

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.

Alfred receives a salary of $2500 per month, and he pays $550 per month in rent. What percentage of his salary is spent on rent?

Let f(x)=2x3−3x2+5x+6f(x)=2 x^{3}-3 x^{2}+5 x+6f(x)=2x3−3x2+5x+6 Find an equation for g , the reflection of f across the y -axis.

Find the range of the function f(x)=x3+x−2f(x)=x^{3}+\sqrt{x-2}f(x)=x3+x−2​ Give your answer in interval notation.

Which of these functions is one-to-one?

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

-The graph above is a slight variation of one of the ten basic functions. Which of the following equations best represents the graph?

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?

Graph the relation defined by the parametric equations x=2t2−4 x=2 t^{2}-4 x=2t2−4 and y=2t y=2 t y=2t . Use a [−5,5] [-5,5] [−5,5] by [−5,5] [-5,5] [−5,5] viewing window and −2t2 -2 t 2 −2t2 .

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

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.

What two functions implicitly define the relation x+∣y∣=2?x+|y|=2 ?x+∣y∣=2? What is the domain?

(a) Find all the zeroes for the function f(x)=3x4−6x2f(x)=3 x^{4}-6 x^{2}f(x)=3x4−6x2 (b) List the intervals where the function f(x)=3x4−6x2f(x)=3 x^{4}-6 x^{2}f(x)=3x4−6x2 is increasing.

Describe how the graph of f(x)=x4−2f(x)=x^{4}-2f(x)=x4−2 can be transformed to the graph of g(x)=(2x)4−2g(x)=(2 x)^{4}-2g(x)=(2x)4−2

Find the inverse relation of $f(x)=\frac{6 x+5}{3 x-1}$

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

Write the equation whose graph can be obtained from the graph of $y=x^{2}$ by a vertical stretching of factor 4 , a reflection through the x -axis, and a vertical shift 5 units up.

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

Let $f(x)=2 x^{3}-3 x^{2}+5 x+6$ Find an equation for g , the reflection of f across the y -axis.

Find the range of the function $f(x)=x^{3}+\sqrt{x-2}$ Give your answer in interval notation.

Graph the relation defined by the parametric equations $x=2 t^{2}-4$ and $y=2 t$ . Use a $[-5,5]$ by $[-5,5]$ viewing window and $-2 t 2$ . $Graph the relation defined by the parametric equations x=2 t^{2}-4 and y=2 t . Use a [-5,5] by [-5,5] viewing window and -2 t 2 .$

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

What two functions implicitly define the relation $x+|y|=2 ?$ What is the domain?

(a) Find all the zeroes for the function $f(x)=3 x^{4}-6 x^{2}$ (b) List the intervals where the function $f(x)=3 x^{4}-6 x^{2}$ is increasing.

Describe how the graph of $f(x)=x^{4}-2$ can be transformed to the graph of $g(x)=(2 x)^{4}-2$