Question

1. Write the exponential function f(x) = -4^(x-2) in the form f(x) = ab^x​

Answer 1

Answer:

$\displaystyle f(x)=-\frac{1}{16}(4^x)$

Step-by-step explanation:

We have the function:

$f(x)=-4^{x-2}$

And we want to convert this to the exponential form:

$f(x)=ab^x$

First, using the power of a product property, we can rewrite our function as:

$f(x)=-(4^x\cdot4^{-2})$

By evaluating the second term, we acquire:

$\displaystyle f(x)=-\big(4^x\cdot \frac{1}{4}^2}\big)=-\big(4^x\cdot \frac{1}{16}\big)$

So, by rearranging, we acquire:

$\displaystyle f(x)=-\frac{1}{16}(4^x)$

As desired.