(Solved): 1/3 First, we note that \( g(x)=f(2 x) \). [Hide explanation] \[ \begin{aligned} g(x) & =\frac{1}{ ...

1/3 First, we note that \( g(x)=f(2 x) \). [Hide explanation] \[ \begin{aligned} g(x) & =\frac{1}{2}(2)^{2 x}-4 \\ & =f(2 x) \end{aligned} \] The expression \( f(k \cdot x) \) when \( |k|>1 \) is a horizontal squash (or compression): The \( x \) -value of every point on the graph of \( y=f(x) \) is divided by \( k \), so the points get closer to the \( y \)-axis. Let's use this information to determine how the graph of \( g \) should look. \( 2 / 3 \quad \) The graph of \( f \) passes through the points \( (3,0) \) and \( (4,4) \).