Which functions have a vertex with a x-value of 0? Select three options. f (x) = |x| f (x) = |x| + 3 f (x) = |x + 3| f (x) = |x| - 6 f (x) = |x + 3| - 6

Step-by-step explanation:

The question does not say anything about what the y value can be. So a surprising choice would be f (x) = abs (x) + 3. This gives you a vertex at (0,3).

A second choice (for the same reason) would be y = abs (x) - 6

The third option can by y = abs (x) which is more in line with what you would expect.

Answer: The correct functions are

(A) f (x) = |x|.

(B) f (x) = |x| + 3.

(D) f (x) = |x| - 6.

Step-by-step explanation: We are given to select he functions that have a vertex with a x-value of 0.

We know that

the vertex of the function f (x) = |x - a| + b is given by (a, b).

Option (A) : f (x) = |x|.

Here, the vertex is given by (0, 0). So, the x-value of the vertex is 0.

This option is correct.

Option (B) : f (x) = |x| + 3.

Here, the vertex is given by (0, 3). So, the x-value of the vertex is 0.

This option is correct.

Option (C) : f (x) = |x + 3|.

Here, the vertex is given by (-3, 0). So, the x-value of the vertex is - 3, not 0.

This option is incorrect.

Option (D) : f (x) = |x| - 6.

Here, the vertex is given by (0, - 6). So, the x-value of the vertex is 0.

This option is correct.

Option (E) : f (x) = |x + 3| - 6.

Here, the vertex is given by (-3, - 6). So, the x-value of the vertex is - 3, not 0.

This option is incorrect.

Thus, the correct functions are

(A) f (x) = |x|.

(B) f (x) = |x| + 3.

(D) f (x) = |x| - 6.