Question

Start with the graph of f(x)=8ˣ. Then write a function that results from the given transformation. Reflect f(x} about the y-axis g(x)=____.

Answer 1

Reflecting the function f(x) = 8^x about the y-axis gives us g(x) = 8^{-x} or alternatively written as g(x) = 1/(8^x).

Step-by-step explanation:

To reflect the function f(x) = 8^x about the y-axis, you'll be looking for a function g(x) that produces the same y-values as f(x) but at the opposite x-values. Reflection over the y-axis implies taking the input value x and using its negation, so g(x) will take every x to -x. The reflected function will be g(x) = 8^{-x}.

Consider the properties of exponents, where we know that a^{-b} = 1/(a^b), we can rewrite g(x) as g(x) = 1/(8^x) for transformation clarity. This results in the graph of f(x) flipped horizontally across the y-axis.