Describe the translation needed to obtain the graph of g(x) = 7x- 8 from the graph of

Question

​f(x) = 7x.

Shift _______ units ______

Answer 1

To obtain the graph of \( g(x) = 7x - 8 \) from the graph of \( f(x) = 7x \), we need to identify the transformation needed.

1. Understanding the functions:

   • \( f(x) = 7x \) is a linear function that passes through the origin (0,0).
   • \( g(x) = 7x - 8 \) is also a linear function, but it has been shifted vertically.

2. Finding the translation:

   • The expression \( -8 \) in \( g(x) \) indicates that we need to shift the graph of \( f(x) \) downward by 8 units.

Therefore, the translation needed to obtain the graph of \( g(x) = 7x - 8 \) from the graph of \( f(x) = 7x \) is:

Shift 8 units down.