Answer the following question

Question

what kind of transformation converts the graph of f(x)=8x+8 into the graph of g(x)=x+8
vertical stretch
vertical shrink
horizontal shrink
horizontal stretch

Answer 1

To find the transformation that converts the graph of \( f(x) = 8x + 8 \) into the graph of \( g(x) = x + 8 \), we can analyze the two functions:

1. The function \( f(x) = 8x + 8 \) represents a line with a slope of 8.
2. The function \( g(x) = x + 8 \) represents a line with a slope of 1.

To see what transformation has occurred in terms of the slope, we can compare the slopes:

• The slope of \( f(x) \): 8
• The slope of \( g(x) \): 1

From the slope of \( f(x) \) (8) to the slope of \( g(x) \) (1), we notice that the slope has decreased by a factor of 8. This can be interpreted as a vertical shrink.

In summary, we have a vertical shrink that converts the graph of \( f(x) \) into \( g(x) \).