1. Lesson 4.7 Graph Linear Functions
Essential Question: What is function notation?

2. Before we start…
Determine whether the pairing is a function. Explain your reasoning.
Hours Worked 10 12 8 16 14
Amount Earned ($) 70 84 56
112 98
Age (Years) 13 14 15
Height (Inches) 50 51 49 56 58 54

3. What is a function?
A pairing so that each input has exactly one output
You can write functions using function notation

4. What is function notation?
You write a function by giving it the name f instead of using y
“the value of f at x” or “f of x”

5. How do you evaluate a function?
Replace the x with the given number and simplify
f (x) is just another name for y. It does not mean f times x.

6. Evaluate 𝑓 𝑥 =−2𝑥+6 when 𝑥=6 Find 𝑓 6 given 𝑓 𝑥 =−2𝑥+6

7. Find 𝑓 −3 given 𝑓 𝑥 =3𝑥−15

8. Find ℎ 7 given ℎ 𝑥 =−7𝑥

9. Find 𝑓 −8 given 𝑓 𝑥 =2𝑥+12

10. Find 𝑝 3 given 𝑝 𝑥 =−8𝑥−2

11. For the function 𝑓 𝑥 =12𝑥+1, find 𝑓 −2 𝑓 0 𝑓 3

12. For the function 𝑝 𝑥 =−3𝑥+5, find 𝑝 −2 𝑝 0 𝑝 3

13. How do you find an x value for a function?
Write the original function.
Substitute the value in for f (x).
Solve the equation for x.

18. For the function 𝑗 𝑥 =4𝑥+11, find the value of x so that 𝑗 𝑥 =−13

19. What is a linear function?
A function whose graph is a line.
Linear functions’ x variable have an exponent of 1.

20. What is a family of functions?
A group of functions with similar characteristics.
Functions that all have the form 𝑓 𝑥 =𝑚𝑥+𝑏 are the family of linear functions.

21. What is a parent function?
The most basic function in a family
The parent linear function is f (x) = x

22. How do you create other functions in the family?
You will perform a transformation to the function. - Shift them - Stretch or shrink them

23. Graph the equation and compare the graph with the graph of 𝑦 = 𝑥.
𝑔 𝑥 =𝑥+3

24. Graph the equation and compare the graph with the graph of 𝑦 = 𝑥.
𝑓 𝑥 =2𝑥

25. Graph the equation and compare the graph with the graph of 𝑦 = 𝑥.
ℎ 𝑥 =−3𝑥

26. Graph the equation and compare the graph with the graph of 𝑦 = 𝑥.
ℎ 𝑥 =2𝑥−3

27. Graph the equation and compare the graph with the graph of 𝑦 = 𝑥.
ℎ 𝑥 =−𝑥+5

29. What is function notation?

30. Ticket Out the Door
Find 𝑑 −2 given 𝑑 𝑥 =− 3 2 𝑥+5