Question

Let f(x) = –7x + 9. Suppose you add 2 to the input of f to create a new function g, then multiply the output of function g by –3 to create function h. What are the slope and y-intercept of the graph of function h?

Slope=?
y-int=?

Answer 1

The slope of the graph of function h is 21 and the y-intercept is 15

To find the slope of the graph of function:

Adding 2 to the input of f:

This creates a new function g(x) = f(x + 2).

According to function composition, g(x) = -7(x + 2) + 9 = -7x - 14 + 9 = -7x - 5.

Lets multiplying the output of g by -3:

This creates a new function h(x) = -3g(x).

According to function composition, h(x) = -3(-7x - 5) = 21x + 15.

The slope of a linear function is the coefficient of the x term in its equation. In the equation h(x) = 21x + 15, the coefficient of x is 21, so the slope is 21

The y-intercept is the value of the function when x = 0. In the equation h(x) = 21x + 15, when x = 0, h(x) = 15, so the y-intercept is 15

Therefore, the slope of the graph of function h is 21 and the y-intercept is 15