Five-Minute Check (over Lesson 2–1) Mathematical Practices Then/Now New Vocabulary Key Concept: Linear Functions Example 1: Identify Linear Functions from Equations Example 2: Real-World Example: Identify Linear Functions from Graphs Example 3: Identify Line Symmetry Example 4: Identify Point Symmetry Lesson Menu

A. function; one-to-one B. function; onto Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. A. function; one-to-one B. function; onto C. function; both D. not a function 5-Minute Check 1

A. function; one-to-one B. function; onto C. function; both Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. A. function; one-to-one B. function; onto C. function; both D. not a function 5-Minute Check 2

A. function; one-to-one B. function; onto Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. {(1, 2), (2, 1), (5, 2), (2, 5)}. A. function; one-to-one B. function; onto C. function; both D. not a function 5-Minute Check 3

Find f(–3) if f(x) = x2 + 3x + 2. A. 20 B. 10 C. 2 D. –2 5-Minute Check 4

What is the value of f(3a) if f(x) = x2 – 2x + 3? A. 3a + 3 B. 3a2 – 6a + 3 C. 9a2 – 2a + 3 D. 9a2 – 6a + 3 5-Minute Check 5

Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure. Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). MP

Linearity and Symmetry Section 2.2

You analyzed continuity of functions. Identify linear and nonlinear functions by examining equations or graphs. Determine whether graphs of functions have line or point symmetry. Then/Now

linear equation linear function nonlinear function line symmetry line of symmetry point symmetry point of symmetry Vocabulary

Key Concept

State whether each function is a linear function. Identify Linear Functions from Equations State whether each function is a linear function. Write yes or no. Explain. g (x) = 2x – 5 Yes g(x) = 2x – 5 is written in the form y = mx + b. m = 2; b = –5 Answer: yes; m = 2, b = –5 Example 1

State whether each function is a linear function. Identify Linear Functions from Equations State whether each function is a linear function. Write yes or no. Explain. B. p (x) = x3 + 2 No p(x) = x3 + 2 cannot be written in the form y = mx + b. Answer: No; x has an exponent other than 1. Example 1

State whether each function is a linear function. Identify Linear Functions from Equations State whether each function is a linear function. Write yes or no. Explain. C. 3y – 21x = 12 Yes 3y – 21x = 12 can be written in the form y = mx + b. y = 7x + 4 m = 7; b = 4 Answer: Yes; the equation is equivalent to y = 7x + 4, m = 7, b = 4 Example 1

Identify Linear Functions from Graphs EARNINGS Malena and Helena work part-time at a smoothie store. The number of hours they worked increased for the first 5 weeks on the job. The graph models Malena’s weekly earnings, and the table models Helena’s weekly earnings, for these 5 weeks. State whether each relation is a linear function. Explain. Real-World Example 2

Identify Linear Functions from Graphs Real-World Example 2

Identify Linear Functions from Graphs Malena’s graph is a linear function. A straight line can be drawn through the points on the graph. Helena’s table is not a linear function. The x values in the table increase at a constant rate; however the y values in the table do not increase at a constant rate. If the points were graphed, a line could not be drawn through the points. Real-World Example 2

Identify Linear Functions from Graphs Answer: Malena: Linear function; a straight line can be drawn through all of the points on the graph. Helena: Nonlinear function; when the ordered pairs from the table are graphed, there is not a single straight line that can be drawn through all of the points. Real-World Example 2

Identify Line Symmetry State whether the graph of the function has line symmetry. If so, identify the line of symmetry. Example 3

Answer: yes; the y-axis or x = 0 Identify Line Symmetry The graph has a line of symmetry. A line can be drawn through the center of the graph and the graph will be identical to the right and the left of the line. x = 0 or the y-axis You can fold the graph on the y-axis and the graph will be the same on each side of the line. Answer: yes; the y-axis or x = 0 Example 3

Identify Point Symmetry State whether the graph of the function has point symmetry. If so, identify the point or points of symmetry. Example 4

Answer: yes; (0, 2) Identify Point Symmetry The graph has a point of symmetry. The graph has a point of symmetry with which you can rotate the graph 180° and the graph will be identical. (0, 2) Is the point you can rotate the graph around. Answer: yes; (0, 2) Example 4