Question 1

Which of the following is the correct graph of  ?
A)

B)

C)

D)

Accepted Answer

C

Question 2

Which choice below is the correct graph of  ?
A)

B)

C)

D)

Accepted Answer

D

Question 3

Choose the function and x- and y-intercepts that best describe the graph. 
A)

B)

C)

D)

Accepted Answer

The function that best describes the graph is a linear function with a negative slope, as the graph is decreasing from left to right. The x-intercept appears to be around x = 3 and the y-intercept appears to be around y = 15. Choice B is the only option that matches these characteristics, with the function y = -3x + 15.

Question 4

Determine whether the table expresses the second variable as a function of the first variable. 
A) No
B) Yes

Accepted Answer

In each row, the second variable (output) is determined by a single value of the first variable (input), which is a characteristic of a function.

Question 5

Which choice below is the correct graph of  ?
A)

B)

C)

D)

Accepted Answer

The answer of Which choice below is the correct graph...

Question 6

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. Match your result to the correct answer below. f(x) = x² + 7x + 12 A) Crosses at (-4, 0) and (3, 0) B) Crosses at (4, 0) and (-3, 0) C) Crosses at (4, 0) and (3, 0) D) Crosses at (-4, 0) and (-3, 0)

Accepted Answer

The polynomial provided seems to be incorrectly formatted, but assuming it's meant to be $f(x) = x^2 + 7x + 12$, the x-intercepts can be found by factoring the quadratic equation. Factoring $x^2 + 7x + 12$ gives $(x+4)(x+3) = 0$, leading to x-intercepts at $x = -4$ and $x = -3$. Since the leading coefficient (1, from $x^2$) is positive and the polynomial is of even degree, the graph touches and turns at each x-intercept, indicating option D is correct.

Question 7

Which piecewise function is represented by the graph? 
A)

B)

C)

D)

Accepted Answer

The answer of Which piecewise function is represented by the...

Question 8

Determine all asymptotes for the graph of the given function. Match your result to the correct answer below. 
A) Vertical : x = -8; Oblique: y = 5x.
B) Vertical : x = 8; Horizontal: x-axis.
C) Vertical : x = 8.
D) Vertical : x = 8; Oblique: y = 5x + 40.

Accepted Answer

The answer of Determine all asymptotes for the graph of...

Question 9

Use the vertical line test to determine which of the following graphs is not the graph of a function.
A)

B)

C)

D)

Accepted Answer

The answer of Use the vertical line test to determine...

Question 10

How are the graphs of f(x) = (x + 10)² and g(x) = -(x + 10)² related? A) The graph of g(x) is the same as that of f(x), but reflected about the x-axis. B) The graph of g(x) is the same as that of f(x), but translated upward by 10 units. C) The graph of g(x) is the same as that of f(x), but translated 10 units to the left. D) The graph of g(x) is the same as that of f(x), but translated 10 units to the right.

Accepted Answer

The graphs of f(x) and g(x) are reflections of each other about the x-axis because g(x) is just f(x) multiplied by -1, which reflects the graph about the x-axis.

Question 11

Find the domain of the given rational function. Match your result to the correct answer below. 
A)

B)

C)

D)

Accepted Answer

The answer of Find the domain of the given rational...

Question 12

Which of the following is the correct graph of the function  ?
A)

B)

C)

D)

Accepted Answer

The answer of Which of the following is the correct...

Question 13

Which choice below is the correct graph of  ?
A)

B)

C)

D)

Accepted Answer

The answer of Which choice below is the correct graph...

Question 14

Which of the following gives the correct domain and range of the relation {(-6, 1), (0, 1)}?
A) Domain = {-6, 0, 1}, range = {1}
B) Domain = {1}, range = {-6, 0}
C) Domain =
 , range = {1}
D) Domain = {-6, 0}, range = {1}

Accepted Answer

The domain of a relation is the set of all the input (x) values, and the range is the set of all the output (y) values. Looking at the given relation {(-6, 1), (0, 1)}, we can see that the domain includes -6 and 0, and the range includes only 1. Therefore, the correct answer is option D, where the domain is {-6, 0} and the range is {1}.

Question 15

Determine whether the relation |6x| = |-7y| is a function.

Accepted Answer

The relation |6x| = |-7y| can be rewritten as |x| = (7/6)|y|. This means for any value of y, there are two values of x that satisfy the equation: one positive and one negative. Therefore, this relation is not a function.

Question 16

Which choice below is the correct graph of  ?
A)

B)

C)

D)

Accepted Answer

The answer of Which choice below is the correct graph...

Question 17

Let f(x) = x² - 2x + 3, g(x) = -2x + 2, and h(x) = |x - 3|. Which of the following is the correct evaluation of ? A) B) C) 2 D)

Accepted Answer

The answer of Let f(x) = x² - 2x +...

Question 18

How are the graphs of  and  related?
A) The graph of g(x) is the same as that of f(x), but stretched along the y-axis by a factor of 9.
B) The graph of g(x) is the same as that of f(x), but translated downward by 9 units.
C) The graph of g(x) is the same as that of f(x), but shrunk along the y-axis by a factor of 9.
D) The graph of g(x) is the same as that of f(x), but translated upward by 9 units.

Accepted Answer

The graphs of the two functions are related by a vertical compression or shrinking by a factor of 9. This can be seen by comparing the y-coordinates of corresponding points on the two graphs. For example, if we take the point (0,1) on the graph of f(x), the corresponding point on the graph of g(x) would be (0,1/9), which is 1/9th the height of the corresponding point on f(x).

Question 19

A gas station charges $1.55 per gallon for regular gasoline. Write an expression for the cost c(g) as a function of the number of gallons g and use this function to determine c(12). Match your results to the correct answer below.
A) c(g) = 1.55g ; c(12) = $20.15
B)
 ; c(12) = $18.60
C) c(g) = 1.55 + g ; c(12) = $13.55
D) c(g) = 1.55g ; c(12) = $18.60

Accepted Answer

The correct expression for the cost c(g) is c(g) = 1.55g, since the cost is simply the price per gallon multiplied by the number of gallons. To find c(12), we substitute g = 12 into the expression, giving c(12) = 1.55(12) = $18.60. Therefore, the correct answer is D.

Question 20

How are the graphs of f(x) = x² and g(x) = x² + 6 related? A) The graph of g(x) is the same as that of f(x), but translated upward by 6 units. B) The graph of g(x) is the same as that of f(x), but translated downward by 6 units. C) The graph of g(x) is the same as that of f(x), but translated 6 units to the right. D) The graph of g(x) is the same as that of f(x), but translated 6 units to the left.

Accepted Answer

The two functions have the same equation except for the constant term added to g(x). This means that the graph of g(x) is the same as that of f(x), but shifted upward by 6 units because the constant term affects only the y-coordinate of the graph, not the x-coordinate.

Quiz 11: Section 1: Functions

Which of the following is the correct graph of ?

Which choice below is the correct graph of ?

Choose the function and x- and y-intercepts that best describe the graph.

Determine whether the table expresses the second variable as a function of the first variable.

Which choice below is the correct graph of ?

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. Match your result to the correct answer below. f(x) = x² + 7x + 12

Which piecewise function is represented by the graph?

Determine all asymptotes for the graph of the given function. Match your result to the correct answer below.

Use the vertical line test to determine which of the following graphs is not the graph of a function.

How are the graphs of f(x) = (x + 10) ² and g(x) = -(x + 10) ² related?

Find the domain of the given rational function. Match your result to the correct answer below.

Which of the following is the correct graph of the function ?

Which choice below is the correct graph of ?

Which of the following gives the correct domain and range of the relation {(-6, 1) , (0, 1) }?

Determine whether the relation |6x| = |-7y| is a function.

Which choice below is the correct graph of ?

Let f(x) = x² - 2x + 3, g(x) = -2x + 2, and h(x) = |x - 3|. Which of the following is the correct evaluation of ?

How are the graphs of and related?

A gas station charges $1.55 per gallon for regular gasoline. Write an expression for the cost c(g) as a function of the number of gallons g and use this function to determine c(12) . Match your results to the correct answer below.

How are the graphs of f(x) = x² and g(x) = x² + 6 related?

Quiz 11: Section 1: Functions

Which of the following is the correct graph of ?

Which choice below is the correct graph of ?

Choose the function and x- and y-intercepts that best describe the graph.

Determine whether the table expresses the second variable as a function of the first variable.

Which choice below is the correct graph of ?

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. Match your result to the correct answer below. f(x) = x2 + 7x + 12

Which piecewise function is represented by the graph?

Determine all asymptotes for the graph of the given function. Match your result to the correct answer below.

Use the vertical line test to determine which of the following graphs is not the graph of a function.

How are the graphs of f(x) = (x + 10) 2 and g(x) = -(x + 10) 2 related?

Find the domain of the given rational function. Match your result to the correct answer below.

Which of the following is the correct graph of the function ?

Which choice below is the correct graph of ?

Which of the following gives the correct domain and range of the relation {(-6, 1) , (0, 1) }?

Determine whether the relation |6x| = |-7y| is a function.

Which choice below is the correct graph of ?

Let f(x) = x2 - 2x + 3, g(x) = -2x + 2, and h(x) = |x - 3|. Which of the following is the correct evaluation of ?

How are the graphs of and related?

A gas station charges $1.55 per gallon for regular gasoline. Write an expression for the cost c(g) as a function of the number of gallons g and use this function to determine c(12) . Match your results to the correct answer below.

How are the graphs of f(x) = x2 and g(x) = x2 + 6 related?

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. Match your result to the correct answer below. f(x) = x² + 7x + 12

How are the graphs of f(x) = (x + 10) ² and g(x) = -(x + 10) ² related?

Let f(x) = x² - 2x + 3, g(x) = -2x + 2, and h(x) = |x - 3|. Which of the following is the correct evaluation of ?

How are the graphs of f(x) = x² and g(x) = x² + 6 related?