Checkpoint: Transforming Exponential Functions Solution

Describe the transformation from f(x) to g(x).

$f (x) = - 3 {(0.67)}^{x} + 1 g (x) = 3 {(0.67)}^{x + 1} - 4$

$b = 0.67, decay \begin{array}{lcl} f (x) & g (x) \\ a = - 3, h = 0, k = 1 & a = 3, h = - 1, k = - 4 \end{array}$

The function is reflected over the x-axis from f(x) to g(x). Then, it shifts left one space and down five spaces.

Note

Q: Are f(x) and g(x) growth or decay? Explain.

A: Both f(x) and g(x) are decay functions because $0 < b < 1 .$  

Q: What would the equation of g(x) be if f(x) was translated 3 units to the right and up 5 units and still reflected over the x-axis?

A: $g (x) = 3 {(0.67)}^{x - 3} + 6$