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
asked 2021-06-26
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.

Answers (1)


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: \(y=0\)

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