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.

the graph of a parabola opening upward and to its right a parabola opening downward

That is, if [latex]y = a + bx + c[/latex] is the general form of a quadratic function, then its parent function is simply [latex]y=x^2[/latex] 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.

where [latex]\large[/latex] is a number

Graph of Constant Function

2. Linear Function

Graph of Parent Function of Linear Function

3. Absolute Value Function

Graph of Parent <a href=Function of Absolute Value Function" width="575" height="463" />

4. Quadratic Function

Graph of Parent Function of Quadratic Function

5. Square Root Function

Graph of Parent Function of Square Root Function

6. Cubic Function

Graph of Parent Function of Cubic Function

7. Cube Root Function

Graph of Parent Function of Cube Root Function

8. Rational Function

Graph of Parent Function- Rational Function

9. Exponential Function

Graph of Parent Function - Exponential Function

10. Logarithmic Function

Graph of Parent Function - Logarithmic Function

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