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

Graph of Constant Function

2. Linear Function

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

Graph of Parent Function of Linear Function

3. Absolute Value Function

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

Graph of Parent Function of Absolute Value Function

4. Quadratic Function

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

Graph of Parent Function of Quadratic Function

5. Square Root Function

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

Graph of Parent Function of Square Root Function

6. Cubic Function

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

Graph of Parent Function of Cubic Function

7. Cube Root Function

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

Graph of Parent Function of Cube Root Function

8. Rational Function

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

Graph of Parent Function- Rational Function

9. Exponential Function

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

Graph of Parent Function - Exponential Function

10. Logarithmic Function

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

Graph of Parent Function - Logarithmic Function
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