Answer: To graph y = f(x) = -(x+4)²+1 and y = 1/f(x) on the same axes, you can follow these steps:
Plot the y-intercept of y = f(x) which is (0,-1)
For y = f(x), the parabola opens downward since the coefficient of x² is -1, thus the vertex is at (-4,1)
Plot the x-intercepts of y = f(x) which are x = 4 and x = -8
The parabola of y = f(x) is symmetric about the y-axis, so the graph will be reflected about the y-axis.
For y = 1/f(x), the x-intercepts will be the same as y = f(x) and the y-intercept is (0,1)
To graph y = 1/f(x), we can start by plotting the x-intercepts and the y-intercept, and then connecting the points.
Label the x-intercepts, y-intercepts, and vertex for both graphs
Shade the regions above the parabola of y = f(x) and below the graph of y = 1/f(x)
Note: It is important to remember that the graph of y = 1/f(x) is a reflection of the graph of y = f(x) across the x-axis, so the y-intercept of y = 1/f(x) is (0,1)
Explanation: