# 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.

**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|}

4. **Quadratic Function**

\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)}