# Graphs of Parent Functions

A parent function is the simplest form that a function can be. Its basic shape is not in any way altered.

For instance, when you see a u-shaped graph that is inverted and vertically stretched, you should still recognize that it is a parabola which has undergone different transformations.

That is, if $y = a{x^2} + bx + c$ is the general form of a quadratic function, then its parent function is simply $y=x^2$ since it’s the simplest of its kind in the family.

## List of Parent Functions

The graphs of the most frequently used parent functions are shown below. It’s a useful mathematical skill to be able to recognize them just by looking at their fundamental shapes.

1. Constant Function

$\large{f\left( x \right) = c}$

where $\large{c}$ is a number

2. Linear Function

$\large{f\left( x \right) = x}$

3. Absolute Value Function

$\large{f\left( x \right) = \left| x \right|}$

$\large{f\left( x \right) = {x^2}}$

5. Square Root Function

$\large{f\left( x \right) = \sqrt x }$

6. Cubic Function

$\large{f\left( x \right) = {x^3}}$

7. Cube Root Function

$\large{f\left( x \right) = \sqrt [3] {x}}$

8. Rational Function

$\large{f\left( x \right) = \Large{{1 \over x}}}$

9. Exponential Function

$\large{f\left( x \right) = {e^x}}$

10. Logarithmic Function

$\large{f\left( x \right) = \ln \left( x \right)}$

Take a quiz:

Identifying Function by its Graph Quiz