Algebra 1-2 Flexbook Q1 Solutions Chapter 2

Transcription

1 Chapter 2: Linear Functions Algebra 1-2 Flexbook Q1 Solutions Chapter Write a Function in Slope-Intercept Form 1. f( 3) = 3; f(0) = 3; f(5) = f( 9) = 4; f(0) = 10; f(9) = f(x) = 5x 3 4. f(x) = 2x f(x) = 7x f(x) = 1 3 x f(x) = 4.2x f(x) = 2x f(x) = 2x 10. f(x) = x 11. sample answer: 4 times the sum of a number and 2 is m/min % %increase 17. w Graph a Line in Standard Form 1. y = 2x + 5

2 2. y = 3 8 x y = 2x 5

3 4. y = 6 5 x 4 5. y = 3 2 x 4

4 6. y = 1 4 x 3 7. x-intercept: (6, 0) y-intercept: (0, 4)

5 8. x-intercept: ( 15, 0) y-intercept: (0, 6) 2 9. x-intercept: (8, 0) y-intercept: (0, 4)

6 10. x-intercept: ( 1, 0) y-intercept: (0, 7) 11. x-intercept: ( 5 2, 0) y-intercept: (0, 3 2 )

7 12. x-intercept: ( 7, 0) y-intercept: (0, 7 2 ) 13. x-intercept: none y-intercept: (0, 3) 14. sample answer: I think converting to slope intercept form is easier because there are less steps. 15. sample answer: I would graph a vertical line at x = 5. There is not y-intercept and the slope is undefined. 2.3 Horizontal and Vertical Line Graphs 1. y = 0 2. x = 0 3. E: x = 6 4. B: y = 2 5. C: y = 7 6. A: y = 5 7. D: x = 4

8 8. 9.

9 Linear Equations in Point-Slope Form 1. y 2 = 1 (x 10) y 125 = 75x 3. y + 2 = 10(x + 8) 4. y 3 = 5(x + 2) 5. y 12 = 13 (x 10) 5 6. y 3 = 0 7. y + 3 = 3 5 x 8. y 0.5 = 6x 9. y 7 = 1 5 x 10. y 5 = 12(x + 2) 11. y 5 = 9 9 (x + 7) OR y + 4 = (x 3) y 6 = x OR y = 1(x 6) 13. y + 9 = 3(x + 2) 14. y 32 = 9 5 x 15. y 20 = 1 1 (x 100) OR y 25 = (x 300) The length of the spring before it is stretched is cm. 16. y 400 = 35 x OR y 50 = 35 (x 20) The depth of the submarine five minutes after it 2 2 started surfacing would be ft. 2.5 Writing and Comparing Functions

10 1. 2.

11 3. 4.

12 5. 6.

13 7. 8.

14 d(t) = t OR d(t) = 30t m = d(t) = t OR d(t) = 20t slope: (#11) m = 30 (#12) m = 20; The distanced traveled each day is larger for the migrating monarch so it flies at a faster rate. y-intercepts: (#11) (0, 1100) (#12) (0, 2000); The y-intercept in this scenario represents the total distance the butterfly must travel, or the amount of miles left to travel on day zero. x-intercepts: (#11) (36 2, 0) (#12) (100, 0); The x-intercept in this scenario represents the amount of 3 time it takes to travel the total migrating distance. Domain: (#11) 0 t 36 2 (#12) 0 t Range: (#11) 0 d(t) 1100 (#12) 0 d(t) f(x) =

15 16. m = The writer needs to sell 4667 books. 2.6 Applications of Linear Models 1. y = 350x ; x= #of months y=amount paid Constraints: The number of months (x) would include integers greater than or equal to zero until the car is paid off. The amount paid would start at $1500 then add an amount of $350 per month until the car is paid off. Domain: {0, 1, 2, 3, } until paid off Range: {1500, 1850, 2150, } until paid off 2. y = 1 x + 17 ; x=# of weeks; y= height of the plant (in) 2 2 Constraints: The number of weeks could be 0 weeks or greater, including a fraction of a week. The height could be greater than or equal to 8.5 inches. Domain: x 0 Range: y 8.5 The height of the rose was 8.5 inches when Anne planted it. 3. y = 1 x + 1; x=weight (lbs.) y=length of spring (m) 40 Constraints: The weight could be 0 lbs. or greater, including fractions of a pound; the length could be greater than or equal to 1 m since that is the length of the spring with no weight attached. There would be a limit to both when the weight would cause the spring to hit the ground. Domain: x 0 Range: y 1 The spring would be 4.5 meters long when Amardeep hangs from it. 4. y = 1 x + 215; x=weight (lbs.) y=distance stretched (ft.) 2 Constraints: The weight could be 0 lbs. or greater, including fractions of a pound; the length would be greater than or equal to 215 ft. which is the length of the cord before it is stretched (within the values that represent a linear function). Domain: x 0 Range: y 215 The expected length of the cord would be 290 ft. for a weight of 150 lbs. 5. y 20 = 1 (x 100); x=weight (g) y=length (cm) 40 Constraints: The weight could be 0 g or greater, including fractions of a gram; the length would be greater than or equal to 17.5 cm which is the length of the cord before it is stretched. Domain: x 0 Range: y y 400 = 35 x; x=time (mins) y=depth (ft) 2 Constraints: The time would be between 0 and minutes (the time it takes to surface) and the depth would be any measure between 400 and 0 feet. Domain: [0, 22.86] Range: [0, 400]

16 7. y 2500 = 6(x 200); x= # of shades sold y=amount $$ made Constraints: It would be possible to sell zero shades and any whole number greater than zero so the positive integers are appropriate; the amount made each month would be a minimum of $1300 plus $6 for each shade thereafter. Domain: positive integers greater than or equal to zero Range: {1300, 1306, 1312, } 8. You can only buy one pound of corn baked fish dinners were sold. 10. Andrew needs to work 36 hours at his $6/hour job to make $ She needs to invest $ or less in the account with 7% interest. 12. y = 6x p = The graph of x = 1.5 is a vertical line at x = 1.5 where the value of x is always 1.5 for any value of y. 15. No it is not a solution. 16. sample answer: (-4, -2); Quadrant III is (-x,-y) 17. m = Rates of Change 1. Slope is the rate of change when considering a linear equation or function because the rate of change is constant. 2. traffic light = B; mending tire = E; hills in order of most steep to least steep: A, F, C, D /hr OR 155mi/3hrs 3 4. $24/week 5. sample answer: An elevator moves at 10 ft/sec. 6. x-intercept: ( 10, 0); y-intercept: (0, 2) 3

17 7. 8. sample answer: 9. Although this can be graphed as a linear function, keep in mind the constraints of dimes and quarters. You can t have a negative amount of either and you can t have a portion of either (i.e dimes). In reality, the graph should be a set of discrete points rather than a continuous linear function.

18 10. domain: { 2, 1, 0, 1, 2}; range: {2, 1, 0, 1, 2} 11. y = x + 1 = 2x subtraction property of equality 3x = 2x 36 substitution property of equality (simplify) 2x 2x subtraction property of equality x = 36 substitution property of equality (simplify) 13. a = 3 Quick Quiz 1. x-intercept: ( 25 35, 0); y-intercept: (0, 3 36

19 2. m = sample answer: Membership has been steadily increasing over the last 10 years. The increase in membership was the same from year to year for the first two years. 2.8 Linear and Non-Linear Function Distinction 1. non-linear 2. linear 3. linear 4. linear 5. non-linear 6. linear 7. linear 8. non-linear

20 9. linear 10. non-linear

21

22

23

24 Comparing Function Models 2.29 linear 2.30 non-linear 2.31 linear 2.32 not quadratic 2.33 quadratic 2.34 not quadratic 2.35 not exponential 2.36 exponential 2.37 exponential 2.38 exponential 2.39 linear 2.40 quadratic