Question

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.

Answer 1

g(x) = a log10(x) = a f(x), meaning that whatever the value of f(x), it will be multiplied by -7. This means that the graph will be reflected across the x-axis (since the values will change sign). Also, multiplying by a factor of 7 stretches the graph vertically.

Therefore, the correct answers are a and d.