# 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  {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)}