Consider the function f(x) = x(x-4).

Question

If the point (2 + c, y) is on the graph of f(x), the following point will also be on the graph of f(x)
A) (c -2,y)
B) (2 - c,y)

Answer 1

To determine if the point (2 + c, y) is on the graph of f(x) = x(x-4), we can substitute the x-value into the function and see if we get the corresponding y-value.

For (2 + c, y) :
f(2 + c) = (2 + c)(2 + c - 4)
= (2 + c)(-2 + c)
= -2(2 + c) + c(2 + c)
= -4 - 2c + 2c + c^2
= -4 + c^2

If we want to determine if another point (x, y) is on the graph, we need to substitute the x-value into the function and see if we get the corresponding y-value.

For (c - 2, y) :
f(c - 2) = (c - 2)(c - 2 - 4)
= (c - 2)(c - 6)
= c(c - 6) - 2(c - 6)
= c^2 - 6c - 2c + 12
= c^2 - 8c + 12

For (2 - c, y) :
f(2 - c) = (2 - c)(2 - c - 4)
= (2 - c)(-2 - c)
= -2(2 - c) - c(2 - c)
= -4 + 2c - 2c + c^2
= -4 + c^2

Comparing the expressions for f(2 + c), f(c - 2), and f(2 - c), we can see that only f(2 + c) = -4 + c^2 is equivalent to the original expression f(x) = x(x - 4).

So the correct answer is:
A) (c - 2, y)