1-7 Notes for Algebra 1 Functions

Function A relationship between the input (domain, x) and output (range, y). In a function, there is exactly one output for each input.

Example 1 pg. 47 Identify Functions Determine whether each relation is a function. Explain. 1.) −2, −8 , 0, 0 , 2, 8 , 4, 16 2.) Domain Range -7 -12 -4 -9 2 3 5

Example 1 pg. 47 Identify Functions Determine whether each relation is a function. Explain. 1.) −2, −8 , 0, 0 , 2, 8 , 4, 16 Function; each element of the domain is paired with exactly one element of the range 2.) Function; each element of the domain is paired with exactly one member of the range Domain Range -7 -12 -4 -9 2 3 5

Example 2 pg. 49 Equations as Functions SCHOOL CAFETERIA there are 3 lunch periods at a school. During the 1st period, 352 students eat. During the 2nd period, 304 students eat. During the 3rd period, 391 students eat. 1.) Make a table showing the number of students for each of the 3 lunch periods. 2.) Determine the domain and range of the function. 3.) Write the data as a set of ordered pairs. Then graph the data. 4.) State whether the function is discrete or continuous. Explain your reasoning.

Example 2 pg. 49 Equations as Functions SCHOOL CAFETERIA there are 3 lunch periods at a school. During the 1st period, 352 students eat. During the 2nd period, 304 students eat. During the 3rd period, 391 students eat. 1.) Make a table showing the number of students for each of the 3 lunch periods. Period 1 2 3 Number of Students 352 304 391

Example 2 pg. 49 Equations as Functions SCHOOL CAFETERIA there are 3 lunch periods at a school. During the 1st period, 352 students eat. During the 2nd period, 304 students eat. During the 3rd period, 391 students eat. 2.) Determine the domain and range of the function. 𝐷= 1, 2, 3 𝑅= 352, 304, 391

Example 2 pg. 49 Equations as Functions SCHOOL CAFETERIA there are 3 lunch periods at a school. During the 1st period, 352 students eat. During the 2nd period, 304 students eat. During the 3rd period, 391 students eat. 3.) Write the data as a set of ordered pairs. Then graph the data. 1, 352 , 2, 304 , 3, 391 400 375 350 325 300 1 2 3

Example 2 pg. 49 Equations as Functions SCHOOL CAFETERIA there are 3 lunch periods at a school. During the 1st period, 352 students eat. During the 2nd period, 304 students eat. During the 3rd period, 391 students eat. 4.) State whether the function is discrete or continuous. Explain your reasoning. Because the points are not connected, the function is discrete.

Example 3 pg. 49 Representation of a Function Determine whether x = -2 represents a function.

Example 3 pg. 49 Representation of a Function Determine whether x = -2 represents a function. Not a function

Example 4 pg. 50 Function Values For 𝑓 𝑥 =3𝑥−4, find each value. 1.) 𝑓 4 2.) 𝑓 −5

Example 4 pg. 50 Function Values For 𝑓 𝑥 =3𝑥−4, find each value. 1.) 𝑓 4 8 2.) 𝑓 −5 -19

Example 5 pg. 50 Nonlinear Function Values If ℎ 𝑡 =1248−160𝑡+16 𝑡 2 find each value. 1.) ℎ 3 2.) ℎ 2𝑧

Example 5 pg. 50 Nonlinear Function Values If ℎ 𝑡 =1248−160𝑡+16 𝑡 2 find each value. 1.) ℎ 3 912 2.) ℎ 2𝑧 1248-320z+64 𝑧 2

1-7 pg. 52 21-47o, 57-75(x3)