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Determine if Odd, Even, or Neither

$f (x) = 5 x^{2} + 6$

Step 1

Find $f (- x)$ .

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Step 1.1

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = 5 {(- x)}^{2} + 6$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the product rule to $- x$ .

$f (- x) = 5 ({(- 1)}^{2} x^{2}) + 6$

Step 1.2.2

Raise $- 1$ to the power of $2$ .

$f (- x) = 5 (1 x^{2}) + 6$

Step 1.2.3

Multiply $x^{2}$ by $1$ .

$f (- x) = 5 x^{2} + 6$

Step 2

A function is even if $f (- x) = f (x)$ .

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Step 2.1

Check if $f (- x) = f (x)$ .

Step 2.2

Since $5 x^{2} + 6 = 5 x^{2} + 6$ , the function is even.

The function is even

Step 3

Enter YOUR Problem

Functions

More step-by-step Algebra examples from this chapter.

Determining if Linear Rewriting as an Equation Rewriting as y=mx+b Solving Function Systems Find the Behavior (Leading Coefficient Test) Finding Ordered Pair Solutions Describing the Transformation Finding the Symmetry Arithmetic of Functions Domain of Composite Functions Finding Roots Using the Factor Theorem Finding All Possible Roots/Zeros (RRT)

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$