Question

Use the test for symmetry to determine if the graph of $y-5x^2=4$ is symmetric about the x-axis.

• A. Symmetrical about x-axis
• B. Not symmetrical about x-axis
• C. Can't be determined
• D. None of these

Answer 1

The correct option is B Not symmetrical about x-axis

The graph is shown in the image.

$y=5x^2+4$ .....equ($1$)

If $f\left(x\right)=f(-x)$, then function is called even function

and if $f\left(x\right)=-f(-x)$, then function is called odd function

put $x=-x$ in equ($1$)

$f(-x)=5(-x{)}^2+4$

$f(-x)=5x^2+4$

since $f\left(x\right)=f(-x)$ ,hence function is even function

$concept$ --

Every EVEN function is symmetric about $Y$-axis and every ODD function is symmetric about $X$-axis.

Because the given function is even, hence it is symmetric about $Y$-axis