Question

# Let f(x)=5⋅2^x a. Write an equation for p, the parent function of f. b. Give the equation for an asymptote of both p and f.

Multivariable functions
Let $$\displaystyle{f{{\left({x}\right)}}}={5}⋅{2}^{{x}}$$
a. Write an equation for p, the parent function of f.
b. Give the equation for an asymptote of both p and f.

The parent function for an exponential function $$\displaystyle{y}={a}{b}^{{2}}$$ is $$\displaystyle{y}={b}^{{2}}$$ so the parent function of f is: $$\displaystyle{p}{\left({x}\right)}={2}^{{x}}$$
The exponential function $$\displaystyle{y}={a}{b}^{{2}}$$ has a horizontal asymptote of $$y=0$$. Since both p and f are of this form, then their asymptotes are both: $$y=0$$