Question

e. write the new equation for each transformation description of the parent function: \\( f(x) = 2(3)^x \\)
a. reflected over the x - axis.
b. vertical shift down 2 units.

Explanation:

Step1: Reflect over x-axis: negate f(x)

$g(x) = -f(x) = -2(3)^x$

Step2: Vertical shift down 2: subtract 2 from f(x)

$h(x) = f(x) - 2 = 2(3)^x - 2$

Answer:

a. $g(x) = -2(3)^x$
b. $h(x) = 2(3)^x - 2$