Question

A function is shown: f(x) = 36x^2 − 1. Choose the equivalent function that best shows the x-intercepts on the graph.

A) f(x) = 18(x^2 − 1)
B) f(x) = (18x + 1)(18x − 1)
C) f(x) = 6(x^2 + 1)
D) f(x) = (6x + 1)(6x − 1)

Answer 1

To find the function that best shows the x-intercepts on the graph, we substitute x with the x-intercepts in each option and check if it equals zero. The equivalent function that best shows the x-intercepts is f(x) = (6x + 1)(6x - 1).

Step-by-step explanation:

To find the function that best shows the x-intercepts on the graph of f(x) = 36x^2 - 1, we need to determine which option will make the expression equal to zero when we substitute x with the x-intercepts. The x-intercepts are the points where the graph intersects the x-axis, so the y-value at those points is zero. Let's evaluate each option:

A) f(x) = 18(x^2 - 1): This option will give us zero when x = ±1, which are the x-intercepts.

B) f(x) = (18x + 1)(18x - 1): This option will give us zero when x = ±1/18, which are not the x-intercepts of the original function.

C) f(x) = 6(x^2 + 1): This option will not give us zero for any value of x.

D) f(x) = (6x + 1)(6x - 1): This option will give us zero when x = ±1/6, which are the x-intercepts of the original function.

Therefore, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x + 1)(6x - 1). Option D is the correct choice.