1. Parent Functions and Transformations
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Parent Functions and Transformations
More Transformations
Writing Equations
Line of Fit
Systems of Equations 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5

2. Identify the function as quadratic, square, root, cubic, exponential.1
Parent Functions
Identify the function as quadratic, square, root, cubic, exponential.
ANSWER

3. 1
Parent Functions
ANSWER
Cubic
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4. BWBAHAB6BPGFE635PAYYMXGWZCKMNM2
Parent Functions
Identify the function family to which f belongs. Compare the graph of f to the graph of its parent function.
ANSWER

5. 2
Parent Functions
ANSWER
Absolute Value Vertical Stretch Translated 3 units to the right Translated 4 units up
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6. 3 Given f(x) = |x|, describe the transformation of: g(x) = 2 + |x - 3|
Parent Functions
Given f(x) = |x|, describe the
transformation of:
g(x) = 2 + |x - 3|
ANSWER

7. Translated 3 units to the right
Parent Functions
ANSWER
Translated 3 units to the right
Translated 2 units up
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8. 4
Parent Functions
Using a graphing calculator, identify and graph the function and its parent function. Then describe the transformations.
𝑓 𝑥 = (𝑥+1)
ANSWER

9. 4 Parent Functions ANSWER Quadratic Translated 1 unit left
Translated 3 units up
Vertical shrink
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10. 5
Parent Functions
Using a graphing calculator, identify and graph the function and its parent function. Then describe the transformations.
𝑔 𝑥 =− 𝑥−1 − 1 2
ANSWER

11. Reflected across the x-axis5
Parent Functions
ANSWER
Absolute Value
Reflected across the x-axis
Translated 1 unit right
Translated 1/2 unit down
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12. 𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 2 𝑢𝑛𝑖𝑡𝑠 𝑑𝑜𝑤𝑛1
More Transformations
Write a function g whose graph represents the indicated transformation of the graph f.
𝑓 𝑥 = 3𝑥+4 +1
𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 2 𝑢𝑛𝑖𝑡𝑠 𝑑𝑜𝑤𝑛
ANSWER

13. 1
More Transformations
ANSWER
𝑔 𝑥 = 3𝑥+4 −1
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14. 2
More Transformations
Write a function g whose graph represents the indicated transformations of the graph of f
𝑓 𝑥 =𝑥
Translated 3 units down followed by a vertical shrink by a factor of 1/3
ANSWER

15. 2
More Transformations
ANSWER
g(x) = 1 3 x - 3
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16. 3
Equations
Write a function g whose graph represents the indicated transformation of the graph of f.
𝑓 𝑥 =|𝑥|
A translation 3 units left followed by a reflection in the y-axis
ANSWER

17. 3
More Transformations
ANSWER
𝑔 𝑥 =|−𝑥+ 3|
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18. 4
More Transformations
Write a function g whose graph represents the indicated transformation of the graph of f.
𝑓 𝑥 = 6𝑥 +3
Horizontal shrink by a factor of 3, followed by a translation 5 units down
ANSWER

19. 4
More Transformations
ANSWER
𝑓 𝑥 = 2𝑥 −2
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20. 5
More Transformations
Write a function g whose graph represents the indicated transformations of the graph.
(4, -3)
ANSWER

21. 5
More Transformations
ANSWER
− 𝑥−4 −3
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22. 1
Writing Equations
Use the graph to write an equation of the line and interpret the slope.
(100, 8)
(300, 2)
ANSWER

23. 1
Writing Equations
ANSWER
𝑦=− 𝑥+10
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24. 2
Writing Equations
Determine whether the data show a linear-relationship. If so, write an equation of a line of fit.
Hours, x 3 7 9 17 20
Battery Life, y 86 61 50 26
ANSWER

25. 2
Writing Equations
ANSWER
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26. 3
Writing Equations
The graph shows the distance Lexi can ride her bike in x hours.
Write an equation of the line
Interpret the slope
How long does it take Lexi to ride 30 miles traveling at the same rate?
ANSWER

27. 3 Writing Equations ANSWER 𝑎) 𝑦=10𝑥
b) That Lexi travels 10 miles per hour on her bike
c) 3 hours
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28. 4
Writing Equations
Alex reads at a constant rate. He reads 735 words in 3 minutes. Write an equation that represents the number of words he reads in x minutes.
How many words can Alex read in 7 minutes?
ANSWER

29. 4
Writing Eqauations
ANSWER
𝑦=245𝑥
1715 words
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30. 5
Writing Equations
Gym A charges a fee of $10 per month plus $5 per fitness class. The table shows Gym B’s fees.
Gym B Fees
Number of classes, x
Total fee ($) 2
$28 5
$40 7
$48 11
$64
a) Which gym charges less per fitness class?
b) After how many fitness classes will the fees of the two gyms be the same?
ANSWER

31. 5 a. Gym B at $4 per fitness class b. 10 classes Writing Equations
ANSWER
a. Gym B at $4 per fitness class
b. 10 classes
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32. 1
Line of Fit
Use the linear regression feature on a graphing calculator to find an equation of the line of best fit for the data. Find and interpret the correlation coefficient.
ANSWER

33. 1 Line of Fit 𝑦=−0.48𝑥+5.68 𝑟=−0.93 ANSWER Strong negative correlation
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34. 2
Line of Fit
The table shows the amount of fruit used to make a smoothie (in ounces) and the total cost (in dollars) of the smoothie.
a) Do the data show a linear relationship?
b) If so write an equation of a line of fit and use it to estimate the total cost of a smoothie that is made using 8 ounces of fruit.
Fruit in a smoothie, x
Total cost, y 2
$2.10 1
$1.50 4
$3.05 7
$4.45 10
$5.95 3
$1.75 6
$4.00
ANSWER

35. 2 Line of Fit 𝑦=0.5𝑥+1 ANSWER The data show a linear relationship
About $5.00
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36. 3
Line of Fit
The table shows the number of bolts and their mass (in grams)
Number of bolts, x
Mass (grams), y 15 61 12 47 9 30 14 59 22
100 4 5 31
140
Write an equation of a line of fit for the data.
Estimate the mass of 20 bolts.
ANSWER

37. 3
Line of Fit
ANSWER
𝑎) 𝑦=5.25𝑥 −16
b) About 89 grams
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38. 4
Line of Fit
Your friend claims the line of best fit for the data shown in the scatter plot has a correlation coefficient close to 1. Is your friend correct?
ANSWER

39. 4
Line of Fit
ANSWER
No, the correlation coefficient will be close to -1 because the data show a negative correlation.
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40. 5
Line of Fit
Use the linear regression feature on a graphing calculator to find:
a) an equation of the line of best fit for the data.
b) interpret the correlation coefficient.
ANSWER

41. 5 Line of Fit ANSWER a) 𝑦=0.42+2.67 b) r = -0.65
The points lie somewhat close to the line.
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42. 1
Systems of Equations
Name the three options for the solutions to a system of equations
ANSWER

43. 1 Systems of Equations ANSWER One solution No solution
Infinitely many solutions
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44. 2
Systems of Equations
Classify the system as consistent or inconsistent.
ANSWER

45. 2 Systems of Equations Inconsistent
ANSWER
Inconsistent
The equations are parallel so it has no solutions.
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46. 3 Systems of Equations Solve the system 6𝑥+8𝑦−6𝑧=62 10𝑥−12𝑦−14𝑧=14
12𝑥−8𝑦+20𝑧=−68
ANSWER

47. 3
Systems of Equations
ANSWER
Exactly one solution
(2, 4, -3)
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48. 4 Recursive Formulas Solve the system 𝑥+𝑦+𝑧=1 6𝑥+9𝑦−12𝑧=14
12𝑥+18𝑦−24𝑧=−11
ANSWER

49. 4
Systems of Equations
ANSWER
No solution
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50. 5 Recursive Formulas Solve the system 2𝑥−2𝑦+2𝑧=12 10𝑥−2𝑦+10𝑧=60
2𝑥+2𝑦+2𝑧=12
ANSWER

51. 5
Recursive Formulas
ANSWER
Infinitely many solutions
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