Question

The graph of y^2=x^2 is symmetric with respect to which axis? a. x-axis c. both b. y-axis d. neither

Answer 1

c. both

Explanation:

Given equation is

Now we need to check if the graph of is symmetric with respect to which axis?

a. x-axis c. both b. y-axis d. neither

We know that if f(-x) reflect the graph about y-axis

so let's change x by -x into given function to see if that equation remains unchanged or not

That is same as previous equation.

Hence given graph is symmetric about y-axis.

We know that if -f(x) reflect the graph about x-axis

so let's change y by -y into given function to see if that equation remains unchanged or not

That is same as previous equation.

Hence given graph is symmetric about x-axis.

So the correct choice is c. both

Answer 2

c. both

Explanation:

Given equation is
`y^2=x^2`

Now we need to check if the graph of
`y^2=x^2` is symmetric with respect to which axis?

a. x-axis c. both b. y-axis d. neither

We know that if f(-x) reflect the graph about y-axis

so let's change x by -x into given function to see if that equation remains unchanged or not

`y^2=(-x)^2`

`y^2=x^2`

That is same as previous equation.

Hence given graph is symmetric about y-axis.

We know that if -f(x) reflect the graph about x-axis

so let's change y by -y into given function to see if that equation remains unchanged or not

`(-y)^2=x^2`

`y^2=x^2`

That is same as previous equation.

Hence given graph is symmetric about x-axis.

So the correct choice is c. both