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)}
