# Is the absolute value of x an even function?

Space and AstronomyBy definition, a function f(x) is even if f(−x)=f(x) , and it is odd if f(−x)=−f(x) . So in the case of the absolute value function, it is clear that **f(−x)=f(x)∀x∈R and hence it is an even function**.

## Is the absolute value of x function even or odd?

even function

It is an **even function**.

## Is an absolute value a function?

**An absolute value function is a function that contains an algebraic expression within absolute value symbols**. Recall that the absolute value of a number is its distance from 0 on the number line.

## What function is the absolute value of x?

Recall that in its basic form **f(x)=|x|**, the absolute value function, is one of our toolkit functions. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Algebraically, for whatever the input value is, the output is the value without regard to sign.

## Is an even function of x?

A function is an even function **if f of x is equal to f of −x for all the values of x**. This means that the function is the same for the positive x-axis and the negative x-axis, or graphically, symmetric about the y-axis.

## Which function is even function?

A function is said to be an even function **if its graph is symmetric with respect to the y-axis**. For example, the function f graphed below is an even function. Verify this for yourself by dragging the point on the x-axis from right to left. Notice that the graph remains unchanged after a reflection across the y-axis!

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