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Parent Functions and Transformations
JEOPARDY 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
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Identify the function as quadratic, square, root, cubic, exponential.
1 Parent Functions Identify the function as quadratic, square, root, cubic, exponential. ANSWER
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1 Parent Functions ANSWER Cubic Jeopardy
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Parent Functions Identify the function family to which f belongs. Compare the graph of f to the graph of its parent function. ANSWER
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2 Parent Functions ANSWER Absolute Value Vertical Stretch Translated 3 units to the right Translated 4 units up Jeopardy
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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
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Translated 3 units to the right
Parent Functions ANSWER Translated 3 units to the right Translated 2 units up Jeopardy
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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
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4 Parent Functions ANSWER Quadratic Translated 1 unit left
Translated 3 units up Vertical shrink Jeopardy
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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
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Reflected across the x-axis
5 Parent Functions ANSWER Absolute Value Reflected across the x-axis Translated 1 unit right Translated 1/2 unit down Jeopardy
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𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 2 𝑢𝑛𝑖𝑡𝑠 𝑑𝑜𝑤𝑛
1 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
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1 More Transformations ANSWER 𝑔 𝑥 = 3𝑥+4 −1 Jeopardy
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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
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2 More Transformations ANSWER g(x) = 1 3 x - 3 Jeopardy
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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
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3 More Transformations ANSWER 𝑔 𝑥 =|−𝑥+ 3| Jeopardy
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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
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4 More Transformations ANSWER 𝑓 𝑥 = 2𝑥 −2 Jeopardy
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5 More Transformations Write a function g whose graph represents the indicated transformations of the graph. (4, -3) ANSWER
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5 More Transformations ANSWER − 𝑥−4 −3 Jeopardy
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1 Writing Equations Use the graph to write an equation of the line and interpret the slope. (100, 8) (300, 2) ANSWER
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1 Writing Equations ANSWER 𝑦=− 𝑥+10 Jeopardy
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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
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2 Writing Equations ANSWER Jeopardy
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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
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3 Writing Equations ANSWER 𝑎) 𝑦=10𝑥
b) That Lexi travels 10 miles per hour on her bike c) 3 hours Jeopardy
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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
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4 Writing Eqauations ANSWER 𝑦=245𝑥 1715 words Jeopardy
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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
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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 Jeopardy
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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
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1 Line of Fit 𝑦=−0.48𝑥+5.68 𝑟=−0.93 ANSWER Strong negative correlation
Jeopardy
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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
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2 Line of Fit 𝑦=0.5𝑥+1 ANSWER The data show a linear relationship
About $5.00 Jeopardy
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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
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3 Line of Fit ANSWER 𝑎) 𝑦=5.25𝑥 −16 b) About 89 grams Jeopardy
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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
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4 Line of Fit ANSWER No, the correlation coefficient will be close to -1 because the data show a negative correlation. Jeopardy
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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
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5 Line of Fit ANSWER a) 𝑦=0.42+2.67 b) r = -0.65
The points lie somewhat close to the line. Jeopardy
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1 Systems of Equations Name the three options for the solutions to a system of equations ANSWER
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1 Systems of Equations ANSWER One solution No solution
Infinitely many solutions Jeopardy
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2 Systems of Equations Classify the system as consistent or inconsistent. ANSWER
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2 Systems of Equations Inconsistent
ANSWER Inconsistent The equations are parallel so it has no solutions. Jeopardy
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3 Systems of Equations Solve the system 6𝑥+8𝑦−6𝑧=62 10𝑥−12𝑦−14𝑧=14
12𝑥−8𝑦+20𝑧=−68 ANSWER
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3 Systems of Equations ANSWER Exactly one solution (2, 4, -3) Jeopardy
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4 Recursive Formulas Solve the system 𝑥+𝑦+𝑧=1 6𝑥+9𝑦−12𝑧=14
12𝑥+18𝑦−24𝑧=−11 ANSWER
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4 Systems of Equations ANSWER No solution Jeopardy
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5 Recursive Formulas Solve the system 2𝑥−2𝑦+2𝑧=12 10𝑥−2𝑦+10𝑧=60
2𝑥+2𝑦+2𝑧=12 ANSWER
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5 Recursive Formulas ANSWER Infinitely many solutions Jeopardy
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