Rational Functions

• (0,0)

• (4,0)

• (5,0)

• (-5,0)

Answer explanation

To find the x-intercept, set f(x) = 0. The function f(x) = 4x/(x-5) equals zero when the numerator is zero. Thus, 4x = 0 leads to x = 0. Therefore, the x-intercept is (0,0).

Tags

CCSS.HSF-IF.C.7D

• (2/3, 0)

• (4,0) and (-2,0)

• (-8,0) and (-1,0)

• (-4,0) and (2,0)

Answer explanation

To find the x-intercepts, set f(x) = 0. This occurs when the numerator is zero: x^2 - 2x - 8 = 0. Factoring gives (x-4)(x+2)=0, so x = 4 and x = -2. Thus, the x-intercepts are (4,0) and (-2,0).

Tags

CCSS.HSF-IF.C.7D

Identify the vertical and horizontal asymptotes.

• x=1, x= 2, y =1, y= 2

• x= 2, x=-2, y = 1

• x=2 y =-1

• x=1 y =2, y =-2

Answer explanation

The vertical asymptotes occur where the function is undefined, which is at x=2 and x=-2. The horizontal asymptote is found by evaluating the end behavior of the function, resulting in y=1. Thus, the correct choice is x=2, x=-2, y=1.

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote of the function given?

• y = 2

• x = 1

• x = 2

• y = -1

Answer explanation

The horizontal asymptote of a function describes its behavior as x approaches infinity. For this function, as x increases, the value approaches y = 2, making it the correct choice for the horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote to this function?

• y=4

• y=0

• y=-2

• y=1

Answer explanation

The horizontal asymptote of a function describes its behavior as x approaches infinity. For this function, as x increases, the value approaches y=4, making it the correct choice.

Tags

CCSS.HSF-IF.C.7D

Where is the hole (also known as a removable discontinuity)?

• x=2

• x=2 and x=3

• x=-3

• x=3

Answer explanation

The hole, or removable discontinuity, occurs at x=2 because the function is undefined at this point, while it is defined elsewhere. Thus, the correct answer is x=2.

Tags

CCSS.HSF-IF.C.7D

What is/are the vertical asymptote(s)?

• x=-2

• x=2 and x=3

• x=-3

• x=3

Answer explanation

The vertical asymptote occurs where the function is undefined. In this case, x=3 is the correct choice, indicating a vertical asymptote at that value, while the other options do not represent vertical asymptotes.

Tags

CCSS.HSF-IF.C.7D

What is the horizontal asymptote?

• y = -4

• y = 1

• x = 1

• y = -6

Answer explanation

The horizontal asymptote represents the value that a function approaches as x approaches infinity. In this case, the correct choice is y = 1, indicating that the function stabilizes at this value for large x.

Tags

CCSS.HSF-IF.C.7D

• y = 0
• y = 1/2
• y = 2
• None

Tags

CCSS.HSF-IF.C.7D

Find the horizontal asymptote.

• None

• y=-2

• y=2

• y=0

Answer explanation

The function does not approach a constant value as x approaches infinity or negative infinity, indicating there is no horizontal asymptote. Therefore, the correct answer is 'None'.

Tags

CCSS.HSF-IF.C.7D