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.The graph is stretched vertically.The graph will shift a units to the right.The graph is compressed.The graph is reflected across the x-axis.The graph will shift a units to the left.
Answer
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.
Explanation
Multiplying f(x) = log₁₀x by −7 multiplies every output by −7. The factor’s magnitude, 7, stretches the graph vertically, and the negative sign reflects it across the x-axis. There is no horizontal shift because the input x has not been changed.
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