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

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

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

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”

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.

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

Find 𝑓 −3 given 𝑓 𝑥 =3𝑥−15

Find ℎ 7 given ℎ 𝑥 =−7𝑥

Find 𝑓 −8 given 𝑓 𝑥 =2𝑥+12

Find 𝑝 3 given 𝑝 𝑥 =−8𝑥−2

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

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

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.

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

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

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.

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

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

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

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

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

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

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

What is function notation?

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