Common Core HSF.IF.C.7.D worksheet

Question 1

Find the vertical asymptote of f(x) = (5x − 4)/(3x − 9). Give the x-value.

Answer 

Question 2

f(x) = (−4x − 7)/(x − 3). Find the vertical asymptote x = ?

Answer 

Question 3

Find the limit as x → ∞ of (−8x² − 6x + 3)/(8x² − 5x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 4

What happens to (6x³ + 2)/(6x² − 3) as x → ∞?

• A. 0
• B. 1
• C. No finite limit (it grows without bound)

Question 5

What are the vertical asymptotes of f(x) = (x² + 1)/(2x² − 72)?

• A. x = 6 and x = −6
• B. x = 6
• C. y = 1/2
• D. There are none

Question 6

Find the horizontal asymptote of f(x) = (6x + 3)/(2x − 10). Give the y-value (fractions allowed).

Answer (as a fraction)

Question 7

f(x) = (4x − 1)/(x − 5). Find the horizontal asymptote y = ?

Answer 

Question 8

Find the limit as x → ∞ of (−5x² + 2x + 3)/(x² − 5x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 9

What happens to (2x + 1)/(5x² − 3) as x → ∞?

• A. 0
• B. 2/5
• C. No finite limit (it grows without bound)

Question 10

What are the vertical asymptotes of f(x) = (2x² + 1)/(4x² − 64)?

• A. x = 16 and x = −16
• B. x = 4 and x = −4
• C. y = 1/2
• D. x = 4

Question 11

Find the horizontal asymptote of f(x) = (x − 1)/(x + 4). Give the y-value (fractions allowed).

Answer (as a fraction)

Question 12

f(x) = (x − 8)/(x − 6). Find the vertical asymptote x = ?

Answer 

Question 13

Find the limit as x → ∞ of (−4x² + 3x + 3)/(5x² + 3x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 14

What happens to (3x³ + 2)/(x² − 3) as x → ∞?

• A. 0
• B. 3
• C. No finite limit (it grows without bound)

Question 15

What are the vertical asymptotes of f(x) = (3x² + 1)/(4x² − 16)?

• A. x = 4 and x = −4
• B. There are none
• C. x = 2
• D. x = 2 and x = −2

Question 16

Find the horizontal asymptote of f(x) = (x − 3)/(x + 2). Give the y-value (fractions allowed).

Answer (as a fraction)