Consider the graphs f (x) = log10x and g (x) = a · log10x.

What happens to the graph of g (x) = a · log10x if a is - 7? Check all that apply.

a. The graph is stretched vertically.

b. The graph will shift a units to the right.

c. The graph is compressed.

d. The graph is reflected across the x-axis.

e. The graph will shift a units to the left.

The answers are a. The graph is stretched vertically and d. The graph is reflected across the x-axis.

Since the parent function f (x) = log10x is multiplied by a constant a that is equal to - 7, the result is a graph for

g (x) = - 7 log10x

This is a vertical stretch of the graph of f (x) because |a|>1.

And since a = - 7 is less than zero, the graph for g (x) = - 7 log10x is reflected across the x-axis.