Module 10 Graphs Of Functions
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This document contains 6 math problems involving graphing functions. Each problem has parts that involve: 1) Completing a table of values for a function. 2) Graphing the function on graph paper using given scales. 3) Finding specific values from the graph. 4) Drawing and finding values from a linear function related to the original. The problems provide practice graphing and extracting information from graphs of quadratic, cubic, rational, and other polynomial functions. The document demonstrates how to set up and solve multi-step math word problems involving graphing functions.
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Module 10 Graphs Of Functions
- 1. PPR Maths nbk MODUL 10 SKIM TIUSYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT” TOPIC : GRAPHS OF FUNCTIONS TIME : 2 HOURS 1. a) Complete Table 1 in the answer space for the equation y = 2x2 – 5x – 3. b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y- axis, draw the graph of y = 2x2 – 5x – 3 for -3 ≤ x ≤ 5. c) From your graph, find i) the value of y when x = -2.4, ii) the value of x when 2x2 – 5x – 3 = 0. d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation 2x2 – 8x = 7 for -3 ≤ x ≤ 5. State these values of x. Answer: a) X -3 -2 -1 0 0.5 1 2 3 4 5 Y 30 4 -3 -6 -5 0 9 22 Table 1 c) i) y = ii) x = d) x =
- 2. PPR Maths nbk 2. a) Complete Table 2 in the answer space for the equation y = x2 – 5x + 4. b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y- axis, draw the graph of y = x2 – 5x + 4 for 0 ≤ x ≤ 8. c) From your graph, find a. the value of y when x = 4.5, b. the value of x when y = 21.75 d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation x2 – 7x + 3 = 0 for 0 ≤ x ≤ 8. State these values of x. Answer: a) X 0 1 2 2.5 3 4 5 6 7 8 Y 4 0 -2 -2 4 10 18 28 Table 2 c) i) y = ii) x = d) x =
- 3. PPR Maths nbk 5 3. a) Complete Table 3 in the answer space for the equation y = . x b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the 5 y-axis, draw the graph of y = for -5 ≤ x ≤ 5. x c) From your graph, find a. the value of y when x = 1.8, b. the value of x when y = -6. d) From your graph, find all the values of x with the condition that the value of y is three times the value of x. Answer: a) X -5 -3 -2 -1 -0.5 0.5 0.9 1.5 2.5 5 Y -1 -1.7 -2.5 -10 10 5.6 3.3 1 Table 3 c) i) y = ii) x = d) x =
- 4. PPR Maths nbk 2 4. a) Complete Table 4 in the answer space for the equation y = x b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 1 units on the y- 2 axis, draw the graph of y = for -4 ≤ x ≤ 4. x c) From your graph, find a. the value of y when x = -1.5, b. the value of x when y = 1.2. d) Draw a suitable straight line on your graph to find all the values of x which 2 3 satisfy the equation = x - 2 for -4 ≤ x ≤ 4. x 4 State these values of x. Answer: a) X -4 -2.5 -2 -1 -0.5 0.5 1 2 2.5 4 Y -0.5 -0.8 -2 -4 4 2 1 0.5 Table 4 c) i) y = ii) x = d) x =
- 5. PPR Maths nbk 5. a) Complete Table 5 in the answer space for the equation y = x3 – 13x + 18 . b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y- axis, draw the graph of y = x3 – 13x + 18 for -4 ≤ x ≤ 4. c) From your graph, find a. the value of y when x = -1.5, b. the value of x when y = 25. d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation x3 – 11x – 2 = 0 for -4 ≤ x ≤ 4. State these values of x. Answer: a) X -4 -3 -2 -1 0 1 2 3 4 Y 6 36 30 18 6 6 30 Table 5 c) i) y = ii) x = d) x =
- 6. PPR Maths nbk 6. a) Complete Table 6 in the answer space for the equation y = x3 + x2 – 12x – 5. b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y- axis, draw the graph of y = x3 + x2 – 12x – 5 for -4 ≤ x ≤ 4. c) From your graph, find a. the value of y when x = 0.5, b. the value of x when 11.9. d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation x3 + x2 – 10x = 0 for -4 ≤ x ≤ 4. State these values of x. Answer: a) X -4 -3 -2 -1 0 1 2 3 4 Y -5 13 7 -5 -15 -17 27 Table 6 c) i) y = ii) x = d) x =
- 7. PPR Maths nbk MODULE 10 – ANSWERS TOPIC: GRAPHS OF FUNCTIONS 1. a) x=-2 y=15 x=0.5 y= -5 x=3 y=0 b) graph 40 35 30 25 y(x) = 2⋅x2-5⋅x-3 20.5 20 15 y(x) = 3⋅x+4 10 5 -10 -5 5 10 -2.4 -0.75 4.75 -5 -10 c) i) x=-2.4 y= 20.5 ii) when 2x2 – 5x – 3 = 0 y=0 Then the values of x is -0.5 and 3 e) y=2x2-5x-3 0=2x2-8x-7 (-) ----------------------- Y= 3x + 4 X 0 3 Y 4 13 From the graph x= -0.75 and 4.75
- 8. PPR Maths nbk 2. a)x=2.5 y=-2.25 x=4 y=0 b)graph 2 c) i) y=1.75 ii) x=7.4 e) straight line y=2x+1 x=0.45 and 6.55 3. a) x=-1 y=-5 x=2.5 y=2 b)graph 16 C 14 12 10 y(x) = 3⋅x 8 6 4 2 A -5 -4 -3 -2 -1 1 2 3 4 5 B -2 5 y(x) = x -4 -6 -8 -10 -12 -14 c) i) x=1.8 y= 2.8 ii) y=-6 x=-0.8 e) The graph is y=3x X 0 2 Y 0 6 The values of x= -1.3 and 1.3
- 9. PPR Maths nbk 4. a) x=-2 y=-1 x=2.5 y=0.8 b) graph c) i) y=-1.3 ii) x=1.7 3 e) The straight line is y= x–2 4 The values of x = -0.75 and 3.45 5. a) x=-3 y=30 x=2 y=0 b) graph 45 40 35 34 30 y=x^3-1 3x+18 25 20 y=-2x+20 15 10 5 3.85 -3.2 -0.25 -6 -4 -2 2 3.35 4 6 c) i) x=-1.5 y=34 -5 ii) y=25 x=3.85 e) y=x3-13x+18 0=x3-11x-2 (-) -------------------------- Y= -2x+20 X 0 4 Y 20 12
- 10. PPR Maths nbk X= -3.2, -0.25 and 3.35 6. a) x=-2 y=15 x=3 y=-5 b) graph 6 c) i) y=10.75 ii) x=-1.5 e) y=-12x-5 x=-3.6, 0 and 2.75