Question

graph the reflection of $f(x) = 1.5(0.5)^x$ across the $y$-axis.
step 1: from the given function, determine the reflected function.
$g(x) = \square (0.5)^{-x}$
options: -1.5, 1.5

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a function \(y = f(x)\) across the \(y\) - axis is \(y=f(-x)\). For the function \(f(x)=1.5(0.5)^{x}\), when we reflect it across the \(y\) - axis, we substitute \(x\) with \(-x\) in the function. So \(g(x)=f(-x)=1.5(0.5)^{-x}\). The coefficient of the exponential term remains \(1.5\) because reflecting across the \(y\) - axis does not change the vertical stretch factor (the coefficient in front of the exponential part), it only changes the input of the exponential function (replaces \(x\) with \(-x\)). So the value in the box should be \(1.5\).

Answer:

\(1.5\)