Question

One of the x-intercepts of the function y = f(x) is 4. Choose the expression which COULD represent f(x).

A) f(x) = (x - 4)
B) f(x) = -(x - 4)
C) f(x) = (x + 4)
D) f(x) = -(x + 4)
E) None of the above.

Answer 1

The expressions that could represent f(x) having an x-intercept of 4 are A) f(x) = (x - 4) and B) f(x) = -(x - 4), since both expressions equal zero when x is 4.

Step-by-step explanation:

If an x-intercept of the function y = f(x) is 4, it means that the function has a root at x = 4, which is the value when the function crosses the x-axis (where y = 0). Therefore, the expression for f(x) must become zero when x is 4. The expressions that fulfill this condition from the given options are:

• f(x) = (x - 4) because f(4) = 4 - 4 = 0.
• f(x) = -(x - 4) because f(4) = -(4 - 4) = 0.

So, both options A and B could represent f(x). Options C and D would result in zero when x is -4, not 4. Therefore, the correct responses are:

• A) f(x) = (x - 4)
• B) f(x) = -(x - 4)