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.

 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.

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step-by-step explanation: