1 / 15

Linear Function

Linear Function. A Linear Function Is a function of the form where m and b are real numbers and m is the slope and b is the y - intercept . The x – intercept is The domain and range of a linear function are all real numbers. Graph. Graph of a Linear Function.

emma-blackwell
Download Presentation

Linear Function

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 Function A Linear Function Is a function of the form where mand bare real numbers andm is the slope and bis the y - intercept. The x – intercept is The domain and range of a linear function are all real numbers. Graph

  2. Graph of a Linear Function The linear function can be graphed using the slope and the y-ntercept Example If m = 3 b = 2 The linear function can be graphed using the x and the y-intercepts

  3. Average Rate of Change The average rate of change of a Linear Function is the constant For example, For f(x)= 5x - 2 , the average rate of change is m =5

  4. Page 121 #15 • f(x) = -3x+4 • The slope is m = -3, the y-intercept b = 4 • The average rate of change is the constant m = -3 • Since m =-3 is negative the graph is slanted downwards. Thus the function is decreasing

  5. Page 121 #19 • f(x) = 3 • f(x)=0x + 3 • m = 0 b = 3 • The average of change is 0 • Since the average rate of change, m = 0 • The function is constant neither increasing or decreasing

  6. Page 121 #21 • To find the zero of f(x), we set f(x) = 0 and solve. • 2x - 8 = 0 • x = 8/2 = 4 • y-intercept • Will graph in class

  7. Page 121 #25 • To find the zero of f(x), we set f(x) = 0 and solve. • x - 8 = 0 • x = 16 • y-intercept • Will graph in class

  8. Linear or Non Linear Function • If a function is linear the slope or rate of change is constant • That is is always the same

  9. Page 121 #28 The rate of change is not constant. Not a Linear Function

  10. Page 121 #32 • Note the rate of change is constant. It is always • m =.5 thus the function is linear

  11. Page 121 #38 If g(x) =-2x+30=0 -2x+30=0 -2x = -30, x = 15 y = g(x) 60=-2(-15)+b b = 30 y =g(x) =-2x +30 If g(x) =-2x+30=20 X = 5 (-15,60) If g(x) -2x+30=60 -2x+30 60 -2x 30, x 15 (5,20) (15,0) If g(x) =-2x+30=60 -2x+30=60 -2x = 30, x = -15 0<2x+30<60 -30 < -2x < 30 15 > x > -15

  12. Page 122 # 44 • Cost Function: C(x) = 0.38x + 5 in dollars • Find Cost for x = 50 minutes • C(50) = .38(50) + 5 = 19+5= $24 • Given Bill, find cost • C(x) = 0.38x + 5 = 29.32 • 0.38x = 24.32 x = 24.32 /.38 x = 62 • Estimated Cost of Monthly Bill, find Maximum minutes • 0.38x + 5 = 60 0.38x = 55 x = 55 /.38 x = 144.8 • Can use as many as 144 minutes

  13. Page 122 # 48Supply(S) and Demand(D) • Equilibrium: Supply = Demand • S(p) = -2000 + 3000p = D(p) =10,000 -1000p • -2000 + 3000p =10,000-1000p • 4000p =12000 p = 3000 • Quantity sold if Demand is less than Supply • If 10,000 -1000p < -2000 +3000p 4000p > 12000 p > 3000 • The price will decrease if the quantity of demand is less than the quantity of supply

  14. Page 122 # 54Straight Line Depreciation • Straight Line Depreciation = Book Value / approximate life • Let V(x) be value of machine after x years • Cost of machine = Book Value = V(0) • V(x) = 120,000 – ($120,000 / 10)x = -12,000x +120,000

  15. Page 122 # 54Straight Line Depreciation(cont) • Book value after 4years = –12000(4)+1210,000 =120000-8000=72000 • After 4 years the machine will be worth $72,000

More Related