which function has two x - intercepts, one at (0, 0) and one at (4, 0)?\n○ f(x)=x(x - 4)\n○ f(x)=x(x + 4)\n○…

Explanation:

Step1: Recall x - intercept formula

The x - intercepts of a function (y = f(x)) are found by setting (f(x)=0).

Step2: Check option 1

Set (f(x)=x(x - 4)=0). By the zero - product property, if (ab = 0), then (a = 0) or (b = 0). So (x=0) or (x - 4=0), which gives (x = 0) or (x=4).

Step3: Check option 2

Set (f(x)=x(x + 4)=0). Then (x=0) or (x+4 = 0), so (x = 0) or (x=-4).

Step4: Check option 3

Set (f(x)=(x - 4)(x - 4)=0). Then (x-4=0), so (x = 4) (a repeated root at (x = 4)).

Step5: Check option 4

Set (f(x)=(x + 4)(x + 4)=0). Then (x+4=0), so (x=-4) (a repeated root at (x=-4)).

Answer:

A. (f(x)=x(x - 4))