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.
I think the answer is 17
kind of a sneaky question.
The graph of g(x) is f(x)-17, so it is shifted -17 units.
But the question explicitly asks how many units down f has been shifted, so the answer is 17
To find how many units the graph of g(x) is shifted down from the graph of f(x), we need to compare the two equations.
First, let's observe the constant terms in the equations:
f(x) = 32x + 8
g(x) = 32x - 9
In f(x), the constant term is +8, which means the graph of f(x) intersects the y-axis at y = 8. Similarly, in g(x), the constant term is -9, meaning the graph of g(x) intersects the y-axis at y = -9.
To determine how much the graph of g(x) is shifted down from the graph of f(x), we need to find the difference in y-intercepts. Subtracting -9 from 8:
8 - (-9) = 8 + 9 = 17.
Therefore, the graph of g(x) is shifted down by 17 units from the graph of f(x).