Cornell Notes Section 1.6 Day 2 Section 1.6 Day 3 Section 1.7 Day 1 Summary (3 sentences) Section 1.6 Day 3 2-3 Questions Section 1.7 Day 1 Highlight, Underline, ?

Section 1.7 Day 2 Functions Algebra 1

Learning Targets Graph a function by creating a table Define a function and function notation Identify a function from a table, ordered pairs, graph, equation, and mapping diagram Identify a function using the vertical line test Construct a function in a table, ordered pairs, graph, and mapping diagram Determine the domain and range of a function from a table, ordered pairs, graph, and mapping diagram Graph a function by creating a table Determine function values from an equation Determine the meaning of function components in a context

Graph a function: Equation To determine if an equation is a function, the easiest method is to graph it. To do this, we will use a table to create ordered pairs Example: Is −3𝑥+𝑦=8 a function? 1. Table 2. Graph 3. Passes VLT Thus, a function! 𝑋 −1 1 2 𝑌 5 4.5 11 14

Example 1: Graphing Is 𝒚= −𝒙 𝟐 a function? 1. Table 2. Graph 3. Passes VLT Thus, a Function X Y −1 1 2 −4

Function Notation Functions can be represented by the notation: 𝒇(𝒙) An equation may look like 𝒚=𝟑𝒙−𝟐 The purpose of this notation is to clearly see the input values and their relationship with the output values. We will take a closer look at this later in the lesson. In function notation, it becomes 𝒇 𝒙 =𝟑𝒙−𝟐

Example 2: Function Values For 𝑓 𝑥 =−4𝑥+7, find each value A) 𝑓(2) 𝑓 2 =−4 2 +7 =−8+7=−𝟏 B) 𝑓 −3 +1 𝑓 −3 =−4 −3 +7 =12+7=𝟏𝟗

Calculator: Function Values 1. Click “y =” 2. Next to 𝑦 1 = type in the function 3. Click “vars” 4. Click the “right button” to “Y-VARS” 5. Click Function (enter) 6. Click 𝑌 1 (enter) 7. Type (#) 8. Click Enter

Example 3: Function Values For 𝑓 𝑥 =2 𝑡 3 , find each value A) 𝑓(1) 𝑓 1 =2 1 3 =2 1 =𝟐 B) 𝑓 3 +3 𝑓 3 +3=2 3 3 +3 =2 27 +3 =54+3=𝟓𝟕

Example 4: Function Values For 𝑓 𝑥 =2𝑥−3, find each value A) 𝑓(𝑦) 𝑓 𝑦 =𝟐𝒚−𝟑 B) 𝑓(𝑟+6) 𝑓 𝑟+6 =2 𝑟+6 −3 =2𝑟+12−3 =𝟐𝒓+𝟗

Interpreting Function Components Let 𝑓(𝑡) be the number of people, in millions, who own cell phones 𝑡 years after 1990. Explain the meaning of the following statements. A) 𝑓 10 =100.3 100,300,000 people own cell phones in 2000 B) 𝑓 𝑎 =20 20,000,000 people own cell phones a years after 1990 C) 𝑓 20 =𝑏 b million people own cell phones in 2010 D) 𝑛=𝑓(𝑡) n million people own cell phones t years after 1990

Example 5: Interpreting Let 𝑓(𝑡) be the number of people waiting in line for a rollercoaster ride, and 𝑡 be measured in hours after the park opens at 8am. Explain the meaning of the following statements A) 𝑓 3 =45 There are 45 people in line at 11am B) 𝑓 𝑡 =60 There are 60 people in line 𝑡 hours after 8am C) 𝑓 5 =𝑎 There are 𝑎 people in line at 1pm D) Write the following in function notation: There are 20 people waiting in line for the ride 4pm. 𝑓 8 =20

Exit Ticket for Homework Worksheet