Explore: Transforming Exponential Functions Solutions

Transforming Exponential Functions Solutions

Before transforming an exponential function, name the value of b to determine if the function represents growth or decay.
As with all other transformations of functions, the values of a, h, and k translate an exponential function in the same way for: $y = a b^{x - h} + k$
a : reflection, vertical stretch $|a| > 1$ or compression $0 < |a| < 1$
h : horizontal shift/translation 
k : vertical shift/translation, the value of k is the horizontal asymptote
 The value of k will also help determine the range of the exponential function.

Describe the transformation from f(x) to g(x). Name the domain and range.

$f (x) = 2 {(8)}^{x + 4} + 6 g (x) = - 2 {(8)}^{x - 3} + 1$

Plan

Determine if the function is growth or decay

Name a, h, k

Compare

Implement

f(x)

$b = 8, growth a = 2, h = - 4, k = 6 domain : \{x | x \in ℝ\} range : \{y | y \in ℝ, y > 6\}$

g(x)

$b = 8, growth a = - 2, h = 3, k = 1 domain : \{x | x \in ℝ\} range : \{y | y \in ℝ, y < 1\}$

From f(x), the function g(x) reflects over the x-axis , shifts right 7 , and down 5 spaces.

Note

Remember you are determining the distance between the h and k-values rather than comparing it to the parent function.

Graph the exponential function. Name the domain and range.

$y = {(0.5)}^{x + 2} - 3$

$a = 1, h = - 2, k = - 3 b = 0.5, decay$

Domain: $\{x | x \in ℝ\}$

Range: $\{y | y \in ℝ, y > - 3\}$

To extend your learning, check out the More to Explore in the Online Lesson.