Question

trevor sketched two graphs. first, he graphed this equation:
\\( y = 5^x \\)
then, he sketched the second graph, which was the same as the first but reflected across the x - axis. write the equation for the second graph.

Explanation:

Step1: Recall reflection over x - axis rule

To reflect a graph of a function \(y = f(x)\) over the \(x\) - axis, we use the transformation rule: if the original function is \(y=f(x)\), the reflected function over the \(x\) - axis is \(y=-f(x)\).

Step2: Apply the rule to the given function

The original function is \(y = 5^{x}\), so when we reflect it over the \(x\) - axis, we replace \(y\) with \(-y\) (or equivalently, multiply the right - hand side by \(- 1\)).
So the equation of the reflected graph is \(y=-5^{x}\).

Answer:

\(y = - 5^{x}\)