### Home > PC3 > Chapter 1 > Lesson 1.1.1 > Problem1-6

1-6.

Recall that functions that have similar graphs and characteristics can be grouped together into what are called families of functions. Some families of functions appear over and over in many different situations that you will encounter in this course and in future math courses. It is important that you learn to recognize which family a particular function belongs to.

The simplest form of each function family is referred to as the parent graph or parent function. The parent graphs you have seen in previous courses are as follows:

Parent

Family

$f \left(x\right) = x$

Linear

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

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

Cubic

$f \left(x\right) = b^{x}$ for $b\ >1$

Exponential

$f \left(x\right) = b^{x}$ for $0

Exponential

$f\left(x\right)=\frac{1}{x}$

Rational

$f(x)=\left|x\right|$

Absolute Value

$f(x)=\sqrt{x}$

Square Root

$f(x)=\sqrt[3]{x}$

Cube Root

$f \left(x\right) = log\left(x\right)$

Logarithmic

Complete the Parent Graph Graphic Organizer. Be sure to sketch accurate graphs since they will be used as models for their respective families. Write down each parent graph’s key features near its graph. Be sure to include domain and range, intercepts, asymptotes, lines of symmetry, and the name of each function. This Parent Graph Graphic Organizer will be used throughout the course.

Use a graphing calculator if you need help. But, you will need to be able to recall the shapes of these functions without a calculator in this course.