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.
is it -17 or 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.
The graph of g(x) is obtained by shifting down the graph of f(x) by 17 units.
To determine the amount by which the graph of f(x) is shifted down to obtain the graph of g(x), we need to compare the constant terms in their respective equations.
In the equation f(x) = 32x + 8, the constant term is +8.
In the equation g(x) = 32x - 9, the constant term is -9.
To find the vertical shift, we compare these constant terms. Since the constant term in g(x) is less than the constant term in f(x), the graph of g(x) is shifted down.
The absolute value of the difference between the two constant terms gives the amount of the vertical shift. In this case, it is |-9 - 8| = 17.
Hence, the graph of g(x) is obtained by shifting down the graph of f(x) by 17 units.