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Lesson Menu Five-Minute Check (over Lesson 2–1) CCSS Then/Now New Vocabulary Example 1:Identify Linear Functions Example 2:Real-World Example: Evaluate a Linear Function Key Concept: Standard Form of a Linear Equation Example 3:Standard Form Example 4:Use Intercepts to Graph a Line

Over Lesson 2–1 Hang onto your HW quiz and compare answers

Over Lesson 2–1 5-Minute Check 1 A.function; one-to-one B.function; onto C.function; both D.not a function Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.

Over Lesson 2–1 5-Minute Check 2 A.function; one-to-one B.function; onto C.function; both D.not a function Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.

Over Lesson 2–1 5-Minute Check 3 A.function; one-to-one B.function; onto C.function; both D.not a function 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)}.

Over Lesson 2–1 5-Minute Check 4 A.20 B.10 C.2 D.–2 Find f(–3) if f(x) = x 2 + 3x + 2.

Over Lesson 2–1 5-Minute Check 5 A.3a + 3 B.3a 2 – 6a + 3 C.9a 2 – 2a + 3 D.9a 2 – 6a + 3 What is the value of f(3a) if f(x) = x 2 – 2x + 3?

CCSS 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). Mathematical Practices 3 Construct viable arguments and critique the reasoning of others.

Then/Now You analyzed relations and functions. Identify linear relations and functions. Write linear equations in standard form.

Vocabulary linear relation nonlinear relation linear equation linear function standard form y-intercept x-intercept We will add these terms to your notes today.

x and y are to the first power

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

Example 1B Identify Linear Functions B. State whether p(x) = x is a linear function. Write yes or no. Explain. Answer: No; this is not a linear function because x has an exponent other than 1.

Example 1C Identify Linear Functions C. State whether t(x) = 4 + 7x is a linear function. Write yes or no. Explain. Answer: Yes; this is a linear function because it can be written as t(x) = mx + b; m = 7, b = 4.

Example 1A A. State whether h(x) = 3x – 2 is a linear function. Explain. A.yes; m = –2, b = 3 B.yes; m = 3, b = –2 C.No; x has an exponent other than 1. D.No; there is no slope.

Example 1B B. State whether f(x) = x 2 – 4 is a linear function. Explain. A.yes; m = 1, b = –4 B.yes; m = –4, b = 1 C.No; two variables are multiplied together. D.No; x has an exponent other than 1.

Example 1C C. State whether g(x, y) = 3xy is a linear function. Explain. A.yes; m = 3, b = 1 B.yes; m = 3, b = 0 C.No; two variables are multiplied together. D.No; x has an exponent other than 1.

Example 2 Evaluate a Linear Function A. METEOROLOGY The linear function f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit f(C) that are equivalent to a given number of degrees Celsius C. On the Celsius scale, normal body temperature is 37  C. What is it in degrees Fahrenheit? f(C) = 1.8C + 32Original function f(37)= 1.8(37) + 32Substitute. = 98.6Simplify. Answer: Normal body temperature, in degrees Fahrenheit, is 98.6°F.

Example 2 Evaluate a Linear Function B. METEOROLOGY The linear function f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit f(C) that are equivalent to a given number of degrees Celsius C. There are 100 Celsius degrees between the freezing and boiling points of water and 180 Fahrenheit degrees between these two points. How many Fahrenheit degrees equal 1 Celsius degree? Divide 180 Fahrenheit degrees by 100 Celsius degrees. Answer: 1.8°F = 1°C

Example 2A A.50 miles B.5 miles C.2 miles D.0.5 miles

Example 2B A.0.6 second B.1.67 seconds C.5 seconds D.15 seconds

Concept

Example 3 Standard Form Write y = 3x – 9 in standard form. Identify A, B, and C. y =3x – 9 Original equation –3x + y =–9Subtract 3x from each side. 3x – y =9Multiply each side by –1 so that A ≥ 0. Answer: 3x – y = 9; A = 3, B = –1, and C = 9

Example 3 Write y = –2x + 5 in standard form. A.y = –2x + 5 B.–5 = –2x + y C.2x + y = 5 D.–2x – 5 = –y

Example 4 Use Intercepts to Graph a Line Find the x-intercept and the y-intercept of the graph of –2x + y – 4 = 0. Then graph the equation. The x-intercept is the value of x when y = 0. The x-intercept is –2. The graph crosses the x-axis at (–2, 0). –2x + y – 4 = 0 Original equation –2x + 0 – 4 = 0 Substitute 0 for y. –2x = 4 Add 4 to each side. x= –2Divide each side by –2.

Example 4 Use Intercepts to Graph a Line Likewise, the y-intercept is the value of y when x = 0. The y-intercept is 4. The graph crosses the y-axis at (0, 4). –2x + y – 4 = 0 Original equation –2(0) + y – 4 = 0 Substitute 0 for x. y = 4 Add 4 to each side.

Example 4 Use Intercepts to Graph a Line Use the ordered pairs to graph this equation. Answer: The x-intercept is –2, and the y-intercept is 4.

Example 4 What are the x-intercept and the y-intercept of the graph of 3x – y + 6 = 0? A.x-intercept = –2 y-intercept = 6 B.x-intercept = 6 y-intercept = –2 C.x-intercept = 2 y-intercept = –6 D.x-intercept = –6 y-intercept = 2

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