Advanced Algebra Tutor Worksheet 1 Graphs of Functions
Advanced Algebra Tutor Worksheet 1 Graphs of Functions
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Advanced Algebra Tutor - Worksheet 1 – Graphs of Functions 1. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑓(𝑥) = 𝑥 2 − 4 2 𝑥
Calculations
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𝑓(𝑥)
2. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑔(𝑥) = 𝑥 3 − 1 𝑥
Calculations
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𝑔(𝑥)
3. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = √𝑥 + 2 2 𝑥
Calculations
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ℎ(𝑥)
4. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑓(𝑥) = 𝑥 2 + 2 4 𝑥
Calculations
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𝑓(𝑥)
5. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑔(𝑥) = 𝑥 3 + 1 𝑥
Calculations
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𝑔(𝑥)
6. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = − √𝑥 + 3 2 𝑥
Calculations
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ℎ(𝑥)
7. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 3 𝑥
Calculations
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𝑓(𝑥)
8. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑔(𝑥) = 𝑥 3 + 2 4 𝑥
Calculations
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𝑔(𝑥)
9. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = √3𝑥 − 2 4 𝑥
Calculations
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ℎ(𝑥)
10. Use a table of values from 𝑥 = −6 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑓(𝑥) = 𝑥 2 + 4𝑥 − 4
𝑥
Calculations
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𝑓(𝑥)
11. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑔(𝑥) = 𝑥 3 − 3 2 𝑥
Calculations
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𝑔(𝑥)
12. Use a table of values from 𝑥 = 0 to 𝑥 = 6 to graph the following function on the quadrant plane below. ℎ(𝑥) = −√𝑥 + 4 𝑥
Calculations
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ℎ(𝑥)
Answers - Advanced Algebra Tutor - Worksheet 1 – Graphs of Functions
1. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑓(𝑥) = 𝑥 2 − 4 2 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations 1 (−3)2 − 4 2 1 (−2)2 − 4 2 1 (−1)2 − 4 2 1 (0)2 − 4 2 1 (1)2 − 4 2 1 (2)2 − 4 2 1 (3)2 − 4 2
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𝑓(𝑥) 0.5 −2 −3.5 −4 −3.5 −2 0.5
2. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑔(𝑥) = 𝑥 3 − 1 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations (−3)3 − 1 (−2)3 − 1 (−1)3 − 1 (0)3 − 1 (1)3 − 1 (2)3 − 1 (3)3 − 1
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𝑓(𝑥) −28 −9 −2 −1 0 7 26
3. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = √𝑥 + 2 2 Answer: 𝑥 0 1 2 3 4 5 6 7
Calculations 1 √0 + 2 2 1 √1 + 2 2 1 √2 + 2 2 1 √3 + 2 2 1 √4 + 2 2 1 √5 + 2 2 1 √6 + 2 2 1 √7 + 2 2
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𝑓(𝑥) 2 2.5 2.7 2.9 3 3.1 3.2 3.3
4. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑓(𝑥) = 𝑥 2 + 2 4 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations 1 (−3)2 + 2 4 1 (−2)2 + 2 4 1 (−1)2 + 2 4 1 (0)2 + 2 4 1 (1)2 + 2 4 1 (2)2 + 2 4 1 (3)2 + 2 4
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𝑓(𝑥) 4.25 3 2.25 2 2.25 3 4.25
5. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑔(𝑥) = 𝑥 3 + 1 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations (−3)3 + 1 (−2)3 + 1 (−1)3 + 1 (0)3 + 1 (1)3 + 1 (2)3 + 1 (3)3 + 1
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𝑓(𝑥) −26 −7 1 1 2 9 28
6. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = − √𝑥 + 3 2 Answer: 𝑥 0 1 2 3 4 5 6 7
Calculations 1 − √0 + 3 2 1 − √1 + 3 2 1 − √2 + 3 2 1 − √3 + 3 2 1 − √4 + 3 2 1 − √5 + 3 2 1 − √6 + 3 2 1 − √7 + 3 2
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𝑓(𝑥) 3 2.5 2.3 2.1 2 1.9 1.8 1.7
7. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 3 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations (−3)2 − 2(−3) − 3 (−2)2 − 2(−2) − 3 (−1)2 − 2(−1) − 3 (0)2 − 2(0) − 3 (1)2 − 2(1) − 3 (2)2 − 2(2) − 3 (3)2 − 2(3) − 3
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𝑓(𝑥) 12 5 0 −3 −4 −3 0
8. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑔(𝑥) = 𝑥 3 + 2 4 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations 1 (−3)3 + 2 4 1 (−2)3 + 2 4 1 (−1)3 + 2 4 1 (0)3 + 2 4 1 (1)3 + 2 4 1 (2)3 + 2 4 1 (3)3 + 2 4
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𝑔(𝑥) −4.75 0 1.75 2 2.25 4 8.75
9. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = √3𝑥 − 2 4 Answer: 𝑥 0 1 2 3 4 5 6 7
Calculations 1 √3(0) − 2 4 1 √3(1) − 2 4 1 √3(2) − 2 4 1 √3(3) − 2 4 1 √3(4) − 2 4 1 √3(5) − 2 4 1 √3(6) − 2 4 1 √3(7) − 2 4
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𝑓(𝑥) −2 −1.6 −1.4 −1.25 −1.1 −1.0 −0.9 −0.8
10. Use a table of values from 𝑥 = −6 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑓(𝑥) = 𝑥 2 + 4𝑥 − 4 Answer: 𝑥 −6 −5 −4 −3 −2 −1 0 1 2 3
Calculations (−6)2 + 4(−6) − 4 (−5)2 + 4(−5) − 4 (−4)2 + 4(−4) − 4 (−3)2 + 4(−3) − 4 (−2)2 + 4(−2) − 4 (−1)2 + 4(−1) − 4 (0)2 + 4(0) − 4 (1)2 + 4(1) − 4 (2)2 + 4(2) − 4 (3)2 + 4(3) − 4
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𝑓(𝑥) 8 1 −4 −7 −8 −7 −4 1 8 17
11. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑔(𝑥) = 𝑥 3 − 3 2 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations 1 (−3)3 − 3 2 1 (−2)3 − 3 2 1 (−1)3 − 3 2 1 (0)3 − 3 2 1 (1)3 − 3 2 1 (2)3 − 3 2 1 (3)3 − 3 2
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𝑓(𝑥) −16.5 −7 −3.5 −3 −2.5 1 10.5
12. Use a table of values from 𝑥 = 0 to 𝑥 = 6 to graph the following function on the quadrant plane below. ℎ(𝑥) = −√𝑥 + 4 Answer: 𝑥 0 1 2 3 4 5 6
Calculations −√0 + 4 −√1 + 4 −√2 + 4 −√3 + 4 −√4 + 4 −√5 + 4 −√6 + 4
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𝑓(𝑥) 4 3 2.6 2.3 2 1.8 1.6
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Advanced Algebra Tutor - Worksheet 1 – Graphs of Functions 1. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑓(𝑥) = 𝑥 2 − 4 2 𝑥
Calculations
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𝑓(𝑥)
2. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑔(𝑥) = 𝑥 3 − 1 𝑥
Calculations
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𝑔(𝑥)
3. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = √𝑥 + 2 2 𝑥
Calculations
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ℎ(𝑥)
4. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑓(𝑥) = 𝑥 2 + 2 4 𝑥
Calculations
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𝑓(𝑥)
5. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑔(𝑥) = 𝑥 3 + 1 𝑥
Calculations
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𝑔(𝑥)
6. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = − √𝑥 + 3 2 𝑥
Calculations
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ℎ(𝑥)
7. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 3 𝑥
Calculations
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𝑓(𝑥)
8. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑔(𝑥) = 𝑥 3 + 2 4 𝑥
Calculations
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𝑔(𝑥)
9. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = √3𝑥 − 2 4 𝑥
Calculations
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ℎ(𝑥)
10. Use a table of values from 𝑥 = −6 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑓(𝑥) = 𝑥 2 + 4𝑥 − 4
𝑥
Calculations
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𝑓(𝑥)
11. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑔(𝑥) = 𝑥 3 − 3 2 𝑥
Calculations
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𝑔(𝑥)
12. Use a table of values from 𝑥 = 0 to 𝑥 = 6 to graph the following function on the quadrant plane below. ℎ(𝑥) = −√𝑥 + 4 𝑥
Calculations
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ℎ(𝑥)
Answers - Advanced Algebra Tutor - Worksheet 1 – Graphs of Functions
1. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑓(𝑥) = 𝑥 2 − 4 2 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations 1 (−3)2 − 4 2 1 (−2)2 − 4 2 1 (−1)2 − 4 2 1 (0)2 − 4 2 1 (1)2 − 4 2 1 (2)2 − 4 2 1 (3)2 − 4 2
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𝑓(𝑥) 0.5 −2 −3.5 −4 −3.5 −2 0.5
2. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑔(𝑥) = 𝑥 3 − 1 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations (−3)3 − 1 (−2)3 − 1 (−1)3 − 1 (0)3 − 1 (1)3 − 1 (2)3 − 1 (3)3 − 1
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𝑓(𝑥) −28 −9 −2 −1 0 7 26
3. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = √𝑥 + 2 2 Answer: 𝑥 0 1 2 3 4 5 6 7
Calculations 1 √0 + 2 2 1 √1 + 2 2 1 √2 + 2 2 1 √3 + 2 2 1 √4 + 2 2 1 √5 + 2 2 1 √6 + 2 2 1 √7 + 2 2
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𝑓(𝑥) 2 2.5 2.7 2.9 3 3.1 3.2 3.3
4. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑓(𝑥) = 𝑥 2 + 2 4 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations 1 (−3)2 + 2 4 1 (−2)2 + 2 4 1 (−1)2 + 2 4 1 (0)2 + 2 4 1 (1)2 + 2 4 1 (2)2 + 2 4 1 (3)2 + 2 4
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𝑓(𝑥) 4.25 3 2.25 2 2.25 3 4.25
5. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑔(𝑥) = 𝑥 3 + 1 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations (−3)3 + 1 (−2)3 + 1 (−1)3 + 1 (0)3 + 1 (1)3 + 1 (2)3 + 1 (3)3 + 1
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𝑓(𝑥) −26 −7 1 1 2 9 28
6. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = − √𝑥 + 3 2 Answer: 𝑥 0 1 2 3 4 5 6 7
Calculations 1 − √0 + 3 2 1 − √1 + 3 2 1 − √2 + 3 2 1 − √3 + 3 2 1 − √4 + 3 2 1 − √5 + 3 2 1 − √6 + 3 2 1 − √7 + 3 2
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𝑓(𝑥) 3 2.5 2.3 2.1 2 1.9 1.8 1.7
7. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 3 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations (−3)2 − 2(−3) − 3 (−2)2 − 2(−2) − 3 (−1)2 − 2(−1) − 3 (0)2 − 2(0) − 3 (1)2 − 2(1) − 3 (2)2 − 2(2) − 3 (3)2 − 2(3) − 3
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𝑓(𝑥) 12 5 0 −3 −4 −3 0
8. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑔(𝑥) = 𝑥 3 + 2 4 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations 1 (−3)3 + 2 4 1 (−2)3 + 2 4 1 (−1)3 + 2 4 1 (0)3 + 2 4 1 (1)3 + 2 4 1 (2)3 + 2 4 1 (3)3 + 2 4
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𝑔(𝑥) −4.75 0 1.75 2 2.25 4 8.75
9. Use a table of values from 𝑥 = 0 to 𝑥 = 7 to graph the following function on the quadrant plane below. 1 ℎ(𝑥) = √3𝑥 − 2 4 Answer: 𝑥 0 1 2 3 4 5 6 7
Calculations 1 √3(0) − 2 4 1 √3(1) − 2 4 1 √3(2) − 2 4 1 √3(3) − 2 4 1 √3(4) − 2 4 1 √3(5) − 2 4 1 √3(6) − 2 4 1 √3(7) − 2 4
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𝑓(𝑥) −2 −1.6 −1.4 −1.25 −1.1 −1.0 −0.9 −0.8
10. Use a table of values from 𝑥 = −6 to 𝑥 = 3 to graph the following function on the quadrant plane below. 𝑓(𝑥) = 𝑥 2 + 4𝑥 − 4 Answer: 𝑥 −6 −5 −4 −3 −2 −1 0 1 2 3
Calculations (−6)2 + 4(−6) − 4 (−5)2 + 4(−5) − 4 (−4)2 + 4(−4) − 4 (−3)2 + 4(−3) − 4 (−2)2 + 4(−2) − 4 (−1)2 + 4(−1) − 4 (0)2 + 4(0) − 4 (1)2 + 4(1) − 4 (2)2 + 4(2) − 4 (3)2 + 4(3) − 4
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𝑓(𝑥) 8 1 −4 −7 −8 −7 −4 1 8 17
11. Use a table of values from 𝑥 = −3 to 𝑥 = 3 to graph the following function on the quadrant plane below. 1 𝑔(𝑥) = 𝑥 3 − 3 2 Answer: 𝑥 −3 −2 −1 0 1 2 3
Calculations 1 (−3)3 − 3 2 1 (−2)3 − 3 2 1 (−1)3 − 3 2 1 (0)3 − 3 2 1 (1)3 − 3 2 1 (2)3 − 3 2 1 (3)3 − 3 2
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𝑓(𝑥) −16.5 −7 −3.5 −3 −2.5 1 10.5
12. Use a table of values from 𝑥 = 0 to 𝑥 = 6 to graph the following function on the quadrant plane below. ℎ(𝑥) = −√𝑥 + 4 Answer: 𝑥 0 1 2 3 4 5 6
Calculations −√0 + 4 −√1 + 4 −√2 + 4 −√3 + 4 −√4 + 4 −√5 + 4 −√6 + 4
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𝑓(𝑥) 4 3 2.6 2.3 2 1.8 1.6
