Question

The functions f(x) and g(x) are described below:

f(x) = 32x + 8
g(x) = 32x − 9

The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units.

Answer 1

The graph of g(x) is obtained by shifting down the graph of f(x) by 17 units.

Explanation:

The functions f(x) and g(x) are linear functions, meaning they will make a straight line when graphed. The are both given in slope-intercept form (y = mx +b) where m = slope and b = y-intercept. In this case, both f(x) and g(x) have a slope of 32, which means their lines are parallel. However, f(x) has a y-intercept of positive 8, while g(x) has a y-intercept of -9. Since the lines are parallel, we can simply shift the graph of f(x) down by 17 total units 8 - (-9) or 8 + 9 = 17.