Which functions are symmetric with respect to the y-axis? check all that apply. f(x) = |x| f(x) = |x| + 3 f(x) = |x + 3| f(x) = |x| + 6 f(x) = |x – 6| f(x) = |x + 3| – 6

The correct options are 1, 2 and 4.

Step-by-step explanation:

The vertex form of an absolute function is

Where, (a,b) is the vertex of the function and x=a is axis of symmetry.

The function is symmetric with respect to the y-axis. It means the axis of symmetry is x=0. It is possible if the value of a in the vertex form is 0.

In option 1,

Here, a=0 and b=0.

Since the value of a=0, therefore it is symmetric with respect to the y-axis.

In option 2,

Here, a=0 and b=3.

Since the value of a=0, therefore it is symmetric with respect to the y-axis.

In option 3,

Here, a=-3 and b=0.

Since the value of a≠0, therefore it is not symmetric with respect to the y-axis.

In option 4,

Here, a=0 and b=6.

Since the value of a=0, therefore it is symmetric with respect to the y-axis.

In option 5,

Here, a=6 and b=0.

Since the value of a≠0, therefore it is not symmetric with respect to the y-axis.

In option 6,

Here, a=-3 and b=-6.

Since the value of a≠0, therefore it is not symmetric with respect to the y-axis.

Hence the correct options are 1, 2 and 4.

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step-by-step explanation:

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