Question

The function k(x) = (gx h)(x) is graphed below, where g is an exponential function and h is a linear function

Answer 1

Given k(x)=g(h(x));

$\begin{gathered} \text{But h(x)=x+1} \\ At\text{ x=-1, } \\ k(-1)=g(h(-1))=g(-1+1)=g(0) \end{gathered}$

Now, let's assess the options.

First,

$\begin{gathered} g(x)=2^x \\ at\text{ x=0,} \\ g(0)=2^0=1\ldots\ldots\ldots\ldots\ldots wrong \end{gathered}$

Also,

$\begin{gathered} g(x)=-2^x \\ g(0)=-2^0 \\ g(0)=-1\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.correct} \end{gathered}$

The formular for g(x) is -2^x