A Library of Parent Functions Objective: To identify the graphs of several parent functions.

Example 1 Write the linear function f for which f(1) = 3 and f(4) = 0.

Writing a Linear Function Write the linear function f for which f(1) = 3 and f(4) = 0. Remember, f(1) = 3 means when x = 1, y = 3 and f(4) = 0 means when x = 4, y = 0. We have two points. We will treat this like a line and find its equation.

Example 1 Write the linear function f for which f(1) = 3 and f(4) = 0. Remember, f(1) = 3 means when x = 1, y = 3 and f(4) = 0 means when x = 4, y = 0. We have two points. We will treat this like a line and find its equation.

You Try Write the linear function f for which f(2) = 5 and f(1) = 2.

You Try Write the linear function f for which f(2) = 5 and f(1) = 2.

Squaring Function We have talked about the look of a 2 nd degree equation and we have called it a parabola. Here are some characteristics. 1.The domain is all real numbers, and the range is either or.

Squaring Function We have talked about the look of a 2 nd degree equation and we have called it a parabola. Here are some characteristics. 1.The domain is all real numbers, and the range is either or. 2.If the coefficient of is positive, it opens up and if the coefficient is negative, it opens down.

Squaring Function We have talked about the look of a 2 nd degree equation and we have called it a parabola. Here are some characteristics. 1.The domain is all real numbers, and the range is either or. 2.If the coefficient of is positive, it opens up and if the coefficient is negative, it opens down. 3.It can have zero, one, or two x-intercepts.

Squaring Function No real roots One real root (2 imaginary) (double root) Two real roots

The Cubic Function We have also talked about a third degree equation and what it looks like. Here are some of its characteristics. 1.The domain and range are all real numbers.

The Cubic Function We have also talked about a third degree equation and what it looks like. Here are some of its characteristics. 1.The domain and range are all real numbers. 2.If the coefficient of is positive, it ends up and to the right and if it is negative, it ends down and to the right.

The Cubic Function We have also talked about a third degree equation and what it looks like. Here are some of its characteristics. 1.The domain and range are all real numbers. 2.If the coefficient of is positive, it ends up and to the right and if it is negative, it ends down and to the right. 3.It can have one, two, or three x-intercepts.

The Cubic Function One real root Two real roots (2 imaginary) (1 double root) Three real roots

The Square Root Function We will take a look at the square root function. This is something that you should recognize and we will talk about it in more depth later.

The Absolute Value Function This is another function that you should recognize. We will do more with it later.

Graphing a Piecewise-Defined Function Sketch the graph of

Graphing a Piecewise-Defined Function You try: Sketch the graph of

Graphing a Piecewise-Defined Function You try: Sketch the graph of

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