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

Answer:

c. both

Step-by-step 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

Answer 2

Answer:

c. both

Step-by-step 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