FINDING HORIZONTAL ASYMPTOTES OF EXPONENTIAL FUNCTIONS WORKSHEET

Answer Key

1)  Three points are (-1, -1/4) (0, -1) and (1, -4).

Horizontal asymptote is y = 0

reflection across x-axis

2)  Three points are (-1, 9/4) (0, 3) and (1, 6).

the horizontal asymptote is at y = 2.

Shift 2 units up

3) Three points are (-1, 16) (0, 64) and (1, 256).

horizontal asymptote is at y = 0.

Shift 3 units left

4)  Three points are (-1, 4) (0, 1) and (1, 1/4).

the horizontal asymptote is at y = 0.

There is no transformation.

Solution:

Parent function :

f(x) = 4^x

Transformation:

Reflection across y-axis and shifting 2 units left

Domain:

All real number

Range:

(0, ∞), {y| y > 0}

Asymptote:

Horizontal asymptote y = 0

6)  

Parent :

f(x) = 4^x

Transformation:

Vertical stretch with the factor of 3 units.

Domain:

All real number

Range:

(0, ∞), {y| y > 0}

Asymptote:

Horizontal asymptote y = 0