|x| = x
always
sometimes
never

Sometimes

Step-by-step explanation:

Lets see

Let x be a positive number

x=3

|3| = 3

True

Let x =0

|0| = 0

True

Let x be a negative number

x=-3

|-3| =-3

3 = -3

False

So this is sometimes true

Sometimes

Step-by-step explanation:

Lets see

Let x be a positive number

x=3

|3| = 3

True

Let x =0

|0| = 0

True

Let x be a negative number

x=-3

|-3| =-3

3 = -3

False

So this is sometimes true

sometimes

Step-by-step explanation:

|x| = x

Lets look at some cases

x>0

Example

3

|3| = 3

3  = 3

Always when x>0

x=0

Example

0

|0| = 0

0  = 0

Always when x=0

x<0

Example

-3

|-3| = -3

3  = -3

Never when x<0

It is only true when x >= 0

So it is sometimes true

Alright! So, your answer is: never a function.

First thing first, let's visualize what a graph symmetric to the x-axis looks like.

Take a look at the first attachment.

Pretty clear, it's symmetric across the x-axis.

To figure out if something is a function or not, use the vertical line test! What you do, is run a vertical line down the graph. Does it eventually give you more than one point? Then it's not a function.

Take a look at this the second attachment.

The vertical line intercepts in 3 different points at once on the top picture. Therefore, it is not a function.

If you're ever uncertain, try the vertical line test. :>

I haven't used in a long while, so pardon if the attachments are a little wonky.

Never

Step-by-step explanation:

Consider x = y^2 That is symmetric around the x axis. Ever value of x except 0 gives an x value that has 2 y values associated with it. See the graph below. I can't think of an example where something symmetric around the x axis is a function.

Alright! So, your answer is: never a function.

First thing first, let's visualize what a graph symmetric to the x-axis looks like.

Take a look at the first attachment.

Pretty clear, it's symmetric across the x-axis.

To figure out if something is a function or not, use the vertical line test! What you do, is run a vertical line down the graph. Does it eventually give you more than one point? Then it's not a function.

Take a look at this the second attachment.

The vertical line intercepts in 3 different points at once on the top picture. Therefore, it is not a function.

If you're ever uncertain, try the vertical line test. :>

I haven't used in a long while, so pardon if the attachments are a little wonky.