Warm-up #4 Given 𝑦=𝑥 2 +5, find y if x = -2 Given x → 1 𝑥−5 , find y if x=2 Given g x = 3𝑥+5 3𝑥−2 , find g(-2)

Homework Function Notation page 3 and 4

Lesson 5.06 Graphing Functions

Look at the Table: determine if the relation is a function x y -3 2 5 4 8

The Vertical Line Test The Vertical Line test is a way to determine if a relation is a function. If a vertical line intersects the relation more than one point, then the relation is NOT a function. Created by: David W. Cummins

If a vertical line passes through a graph more than once, the graph is not the graph of a function. Hint: Pass a pencil across the graph held vertically to represent a vertical line. The pencil crosses the graph more than once. This is not a function because there are two y-values for the same x-value.

Yes it is a function

Not a function

Not a function

Yes it is a function

Yes it is a function

Problem 1: Find an equation of a linear function {(0, -3), (1, 1), (2, 5)} Step 1: Choose any two points to find the slope. 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐− 𝒙 𝟏 Step 2: You need one ordered pair and the slope value. Plug it into the point-slope form 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) Step 3: Simplify the equation into slope-intercept form y = mx + b

{(0, -3), (1, 1), (2, 5)} Step 1: 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐− 𝒙 𝟏 Step 3: y = mx + b

Plot the relation. If the relation is a linear function, then write an equation for it. 1) {(-3, 5), (-4, 5), (0, 8)} 2) {(-3, 5), (0, 3), (3, 1)}

Function? Look at the function. Is there any number x for which 𝟏 𝒙+𝟖 does not make sense? Recap: look at the denominator. What makes a fraction undefined? Step 1: set the denominator equal to 0 Step 2: solve for the variable Step 3: state the domain

Practice Problems x → 4 3𝑥−2 f x = 3𝑥+5 −2𝑥+5 Find the domain of each function x → 4 3𝑥−2 f x = 3𝑥+5 −2𝑥+5

Function? Look at the function. Is there any number x for which 𝒈 𝒙 = 𝒙−𝟐 does not make sense? Recap: you cannot have a NEGATIVE number in the square root

Practice Problems Find the domain of each function x → −2𝑥 g x = 𝑥+4