Question

If in the equation y = f(x), f(x) is even function then

• A. $f(-x)=-f\left(x\right)$
• B. $f(-x)=f\left(x\right)$
• C. Its graph is symmetric about y-axis.
• D. If (x, y) is a point on its graph, then (-x, y) is also on the same graph.

Answer 1

Answer: (B), (C), (D)

The correct options are
B $f(-x)=f\left(x\right)$
C Its graph is symmetric about y-axis.
D If (x, y) is a point on its graph, then (-x, y) is also on the same graph.

A function f(x) is said to be even, if it remains unchanged after replacing x in the equation with -x.
$i.e.,f(-x)=f\left(x\right)$
As both x and -x give the same output from the function. Hence, its graph will be symmetric about y-axis.

There will be two values of x for one value of y, one will be +x and other will be -x. Hence, in the graph if (x, y) is a point, then (-x, y) will also be a point.