Answer:
B. g(x)=5f(x)
Explanation:
The graph of function g is a vertical stretch of the graph of function f by a factor of 5. Let analyse all the possible answers:
- For C and D are the same transformation and they are only be transformed horizontally and be compressed over the x-axis.
When 0 < |a| < 1 (when a is between 0 and 1), the function is compressed vertically by a dilation factor of |a|.
When |a| > 1 (when a is greater than 1), the function is stretched vertically by a dilation factor of |a|.
Lastly, when a is negative, the function is reflected in the x-axis and then it is stretched or compressed vertically by a dilation factor of |a|.
- For A, the parameter 0 < a =1/5 < 1, so it will make the original function compress vertically over the y-axis
- For B, the parameter a= 5> 0, so it will make the original function stretch vertically over the y-axis
Hence, we choose B