4.1 Identifying Linear Functions

Transcription

1 Warm-up Solve the equation for y. Then graph. 1. 2x - 3y = Identifying Linear Functions I can... 1.) identify a linear function by a graph 2.) identify a linear function by ordered pairs (table) 3.) identify a linear function by an equation 4.) graph a linear function 5.) graph a linear function that represents a real world situation along with giving the domain and range 1

2 Linear Functions Describe many realworld situations, such as distances traveled at a constant speed. Linear Function Graphing Each domain value (x value) is paired with exactly one range value (y value). Forms a straight line when graphed on a coordinate plane. 2

3 Linear Function Table/List of Ordered Pairs A constant change in x corresponds to a constant change in y. Linear Function Linear Equation A function is linear if it is described by a linear equation. Linear Equation: Any equation that can be written in standard form. Ax + By = C 2x + 3y = 5 5x + y = 10 x 4y = 7 3

4 I can identify a linear function by a graph Example 1: Identify whether each graph represents a function. Explain. If the graph does represent a function, is the function linear? a. b. c. Linear Linear Linear I can identify a linear function by a graph Checkpoint: Identify whether each graph represents a function. Explain. If the graph does represent a function, is the function linear? Linear Linear 4

5 I can identify a linear function by ordered pairs (table) Example 2: Tell whether each set of ordered pairs satisfies a linear function. Explain. a. {(2, 4), (5, 3), (8, 2), (11, 1)} b. {( 10, 10), ( 5, 4), (0, 2), (5, 0) I can identify a linear function by ordered pairs (table) Partner Check: Tell whether each table satisfies a linear function. Explain

6 Another way to determine whether a function is linear is to look at its equation. Standard Form of a Linear Equation Ax + By = C where A, B, and C are real numbers, & A and B are not both zero x and y both have exponents of 1 x and y are not multiplied together x and y do not appear in denominators, exponents, or radical signs Linear 3x + 2y = 10 x y = 0 Not Linear 3xy + x = 1 x 3 + y = 1 I can identify a linear function by an equation Example 3: Tell whether each function is linear. a. y = x + 3 b. 5x = 3y + 10 c. y = x

7 I can identify a linear function by an equation Checkpoint: Tell whether each function is linear. 3. y = 5x 9 4. xy = y = 2 x Real World Situations The domain and range may be restricted. For example, some quantities cannot be negative, such as time. Domain: x 0 Range: y 0 7

8 I can graph a linear function I can graph a linear function that represents a real world situation along with giving the domain and range Example 4: Sue rents a manicure station in a salon and pays the salon owner $5.50 for each manicure she gives. The amount Sue pays each day is given by f(x) = 5.50x, where x is the number of manicures. Graph this function and give its domain and range. x f(x) = 5.50x Domain: Range: I can graph a linear function I can graph a linear function that represents a real world situation along with giving the domain and range Checkpoint: At another salon, Sue can rent a station for $10.00 per day plus $3.00 per manicure. The amount she would pay each day is given by f(x) = 3x + 10, where x is the number of manicures Graph this function on the graph above and give its domain and range. x f(x) = 3x + 10 Domain: Range: 8

9 Determining Whether a Function is Linear From Its graph From Its equation From a list of ordered pairs 9