1.5 – library of functionsGoal: to recognize basic shapes/properties of graphs of different types of functions

We know many functions and their properties already…

Let’s remember and refer to their parent functionsLinear function: f(x) = x or f(x) = cQuadratic function(squaring): f(x) = x2

Cubic function: f(x) = x3

Radical function(square root): f(x) = Rational function(reciprical): f(x) =

*all the graphs and their properties are defined starting on page 52.

Piecewise-defined functionsLet’s graph the function we evaluated in section 1.3…

𝑓 (𝑥 )={ 𝑥2+2 ,𝑥<272≤𝑥 ≤42𝑥−4 ,𝑥>4

On your own, please graph:

𝑓 (𝑥 )={2𝑥+3 , 𝑥≤1− 𝑥+4 ,𝑥>1

Let’s graph one more…

𝑓 (𝑥 )={2𝑥 ,(−∞,−1)2 𝑥2 ,¿−𝑥+3 ,(2 ,∞)

HOMEWORK:

pg. 56 #’s 3,43, 45, 47, 49, 67, 68

*finish warm up problems too!

Let’s recall the “subway problem”….

What did the graph look like?

Does anyone remember the data?

This graph is called a STEP FUNCTION

The most common step function is the GREATEST INTEGER FUNCTION

*means the greatest integer less than or equal to x

Evaluating the Greatest integer function…

=? =?

=?

=?

= ? =?

Let’s practice evaluating and graphing greatest integer functions…

+1 for f(-1, 2, 1.5,

Partner Work:

Complete Packet

Now please try # 30, 32 on page 56

Homework: Day 2

Pg. 56 #’s 7, 31, 33, 35, 39, 41, 53-62, 63, 66