1 / 20

13-4

Linear Functions. 13-4. Course 3. Warm Up. Problem of the Day. Lesson Presentation. Linear Functions. 13-4. Course 3. Warm Up Determine if each relationship represents a function. 1. 2. y = 3 x 2 – 1 3. For the function f ( x ) = x 2 + 2, find f (0), f (3), and f (–2). yes.

asteinberg
Download Presentation

13-4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Linear Functions 13-4 Course 3 Warm Up Problem of the Day Lesson Presentation

  2. Linear Functions 13-4 Course 3 Warm Up Determine if each relationship represents a function. 1. 2.y = 3x2 – 1 3. For the function f(x) = x2 + 2, find f(0), f(3), and f(–2). yes yes 2, 11, 6

  3. Problem of the Day Take the first 20 terms of the geometric sequence 1, 2, 4, 8, 16, 32, . . . .Why can’t you put those 20 numbers into two groups such that each group has the same sum? All the numbers except 1 are even, so the sum of the 20 numbers is odd and cannot be divided into two equal integer sums.

  4. Learn to identify linear functions.

  5. Vocabulary linear function function notation

  6. Reading Math f(x) is read “f of x.” f(1)is read “f of 1.” A linear function can be described by a linear equation. You can use function notation to show that the output value of the function f, written f(x), corresponds to the input value x. The graph of a linear function is a line. The linear function f(x) = mx +b has a slope of m and a y-intercept of b.

  7. y 4 2 x -4 -2 2 4 -4 Additional Example 1: Identifying Linear Functions Determine whether the function f(x) = 2x3 is linear. f(x) = 2x3 Graph the function. f(x) = 2x3 does not represent a linear function because its graph is not in a straight line.

  8. y 4 2 x -4 -2 2 4 -2 -4 Check It Out: Example 1 Determine whether the function f(x) = -2x + 4 is linear. f(x) = –2x + 4 Graph the function. f(x) = -2x + 4 does represent a linear function because its graph is in a straight line. It has a slope of -2 and a y-intercept of 4.

  9. Additional Example 2A: Writing the Equation for a Linear Function Write a rule for the linear function. Step 1 Identify the y-intercept b from the graph. b = 2 Step 2 Locate another point on the graph, such as (1, 4). Step 3 Substitute the x- and y-values of the point into the equation, f(x) = mx + b, and solve for m.

  10. Additional Example 2A Continued f(x) = mx + b 4 = m(1) + 2(x, y) = (1, 4) 4 = m + 2 – 2 – 2 2 = m The rule is f(x) = 2x + 2.

  11. y2 – y1 m = = = = 3 x2 – x1 10 – 4 3 – 1 6 2 Additional Example 2B: Writing the Equation for a Linear Function Write a rule for the linear function. Step 1 Locate two points. (1, 4) and (3, 10) Step 2 Find the slope m. Step 3 Substitute the x- and y-values of the point into the equation, f(x) = mx + b, and solve for b.

  12. Additional Example 2B Continued f(x) = mx + b 4 = 3(1) + b(x, y) = (1, 4) 4 = 3 + b – 3– 3 1 = b The rule is f(x) = 3x + 1.

  13. y 4 2 x -4 -2 2 4 -4 Check It Out: Example 2A Write a rule for the linear function. Step 1 Identify the y-intercept b from the graph. b = 1 Step 2 Locate another point on the graph, such as (5, 2). Step 3 Substitute the x- and y-values of the point into the equation, f(x) = mx + b, and solve for m.

  14. 1 1 5 5 m = The rule is f(x) = x + 1. Check It Out: Example 2A Continued f(x) = mx + b 2 = m(5) + 1(x, y) = (5, 2) 2 = 5m + 1 – 1 – 1 1 = 5m

  15. y2 – y1 m = = = = 1 x2 – x1 6 – 5 1 – 0 1 1 Check It Out: Example 2B Write a rule for the linear function. Step 1 Locate two points. (0, 5) and (1, 6) Step 2 Find the slope m. Step 3 Substitute the x- and y-values of the point into the equation, f(x) = mx + b, and solve for b.

  16. Check It Out: Example 2B Continued f(x) = mx + b 5 = 1(0) + b(x, y) = (0, 5) 5 = b The rule is f(x) = x + 5.

  17. Example 3: Money Application A video club cost $15 to join. Each video that is rented costs $1.50. Find a rule for the linear function that describes the total cost of renting videos as a member of the club, and find the total cost of renting 12 videos. f(x) = mx + 15 The y-intercept is the cost to join, $15. 16.5 = m(1) + 15 With 1 rental the cost will be $16.50. 16.5 = m + 15 The rule for the function is f(x) = 1.5x + 15. After 12 video rentals, the cost will be f(12) = 1.5(12) + 15 = 18 + 15 = $33. –15– 15 1.5 = m

  18. Check It Out: Example 3 A book club has a membership fee of $20. Each book purchased costs $2. Find a rule for the linear function that describes the total cost of buying books as a member of the club, and find the total cost of buying 10 books. f(x) = mx + 20 The y-intercept is the cost to join, $20. With 1 book purchase the cost will be $22. 22 = m(1) + 20 22 = m + 20 The rule for the function is f(x) = 2x + 20. After 10 books purchases, the cost will be f(10) = 2(10) + 20 = 20 + 20 = $40. –20– 20 2 = m

  19. Lesson Quiz: Part I Determine whether each function is linear. 1. f(x) = 4x2 2.f(x) = 3x + 1 Write the rule for the linear function. not linear linear 1 2 f(x) = x- 1

  20. Lesson Quiz: Part II Write the rule for each linear function. 2. 3. Andre sells toys at the craft fair. He pays $60 to rent the booth. Materials for his toys are $4.50 per toy. Find a rule for the linear function that describes Andre's expenses for the day. Determine his expenses if he sold 25 toys. f(x) = 3x – 1 f(x) = 4.50x + 60; $172.50

More Related