DESCRIBING TRANSFORMATIONS OF EXPONENTIAL FUNCTIONS WORKSHEET

Describe the transformation that map the function y = 2^x on each of the following functions.

Problem 1 :

y = 2^x - 2

Solution

Problem 2 :

y = 2^x+3

Solution

Problem 3 :

y = 4^x

Solution

Problem 4 :

y = 3(2^{x - 1}) + 1

Solution

Describe the transformation that map into the function

y = 8^x

on to each function.

Problem 5 :

y = (1/2) 8^x

Solution

Problem 6 :

y = -8^x

Solution

Problem 7 :

y = 8^-2x

Solution

Using the parent graph of f(x) = 4^x, describe the transformation of each function.

Problem 8 :

f(x) = -2(4^{x + 3}) - 5

Solution

Problem 9 :

f(x) = (4^{2x + 6}) + 2

Solution

Problem 10 :

f(x) = (4^{-3x + 12}) + 1

Solution

Problem 11 :

f(x) = (4^{(1/2)x - 2}) + 3

Solution

Problem 12 :

f(x) = (1/3)(4^{(1/3)x + 3}) - 4

Solution

Answer Key

1) shifting 2 units down

2) shifting 3 units left

3) horizontal compression by the factor of 2.

4) vertical stretch with the factor of 3.

No reflection

Translation of 1 unit right and 1 unit up.

5) vertical compression by the factor of 1/2.

6) reflection across x-axis.

7) horizontal compression with reflection across y-axis.

8) Vertical stretch of factor 2 ==> reflection across x-axis => move left 3 units and down 5 units.

9) Horizontal compression of 2 units. No reflection. Move horizontally 6 units left and 2 unit up.

10) Horizontal compression of 3 units. Reflection across y-axis. Move horizontally 12 units left and 1 unit up.

11) Horizontal stretch of 1/2 units. No reflection. Move horizontally 2 units right and 3 units up.

12) Horizontal stretch of 1/3 units. No reflection. Move horizontally 3 units left and 4 units down.

DESCRIBING TRANSFORMATIONS OF EXPONENTIAL FUNCTIONS WORKSHEET

Answer Key

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