1. 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)

2. Homework
Function Notation page 3 and 4

3. Lesson 5.06 Graphing Functions

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

5. 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

6. 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.

7. Yes it is a function

8. Not a function

9. Not a function

10. Yes it is a function

11. Yes it is a function

12. 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

13. {(0, -3), (1, 1), (2, 5)} Step 1: 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐− 𝒙 𝟏
Step 3: y = mx + b

14. 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)}

15. 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

16. 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

17. 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

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