JEOPARDY: Parent Functions and Transformations
A series of challenges related to identifying parent functions, graph transformations, and system of equations in a Jeopardy-style format. Test your knowledge in recognizing function families, graph translations, and more. Learn about quadratic, cubic, absolute value, and exponential functions through interactive examples and answers.
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Presentation Transcript
JEOPARDY Parent Functions and Transformations 1 2 More Writing Equations 1 2 3 4 5 Systems of Equations 1 2 3 4 5 Line of Fit Transformations 1 2 3 4 5 1 1 1 1 1 1 2 3 4 5 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5
1 Parent Functions Identify the function as quadratic, square, root, cubic, exponential. ANSWER
1 Parent Functions ANSWER Cubic Jeopardy Jeopardy
BWBAHAB6BPGFE635PAYYMXGWZCKMNM2 2 Parent Functions Identify the function family to which f belongs. Compare the graph of f to the graph of its parent function. ANSWER
2 Parent Functions ANSWER Absolute Value Vertical Stretch Translated 3 units to the right Translated 4 units up Jeopardy
3 Parent Functions Given f(x) = |x|, describe the transformation of: g(x) = 2 + |x - 3| ANSWER
3 Parent Functions ANSWER Translated 3 units to the right Translated 2 units up Jeopardy
4 Parent Functions Using a graphing calculator, identify and graph the function and its parent function. Then describe the transformations. 3 4(? + 1)2 + 3 ? ? = ANSWER
4 Parent Functions ANSWER Quadratic Translated 1 unit left Translated 3 units up Vertical shrink Jeopardy
5 Parent Functions Using a graphing calculator, identify and graph the function and its parent function. Then describe the transformations. ? ? = ? 1 1 2 ANSWER
5 Parent Functions ANSWER Absolute Value Reflected across the x-axis Translated 1 unit right Translated 1/2 unit down Jeopardy
1 More Transformations Write a function g whose graph represents the indicated transformation of the graph f. ? ? = 3? + 4 + 1 ??????????? 2 ????? ???? ANSWER
1 More Transformations ANSWER ? ? = 3? + 4 1 Jeopardy
2 More Transformations Write a function g whose graph represents the indicated transformations of the graph of f ? ? = ? Translated 3 units down followed by a vertical shrink by a factor of 1/3 ANSWER
2 More Transformations ANSWER g(x) = 1 3x - 3 Jeopardy
3 Equations Write a function g whose graph represents the indicated transformation of the graph of f. ? ? = |?| A translation 3 units left followed by a reflection in the y-axis ANSWER
3 More Transformations ANSWER ? ? = | ? + 3| Jeopardy
4 More Transformations Write a function g whose graph represents the indicated transformation of the graph of f. ? ? = 6? + 3 Horizontal shrink by a factor of 3, followed by a translation 5 units down ANSWER
4 More Transformations ANSWER ? ? = 2? 2 Jeopardy
5 More Transformations Write a function g whose graph represents the indicated transformations of the graph. (4, -3) ANSWER
5 More Transformations ANSWER ? 4 3 Jeopardy
1 Writing Equations Use the graph to write an equation of the line and interpret the slope. (100, 8) (300, 2) ANSWER
1 Writing Equations ANSWER 3 ? = 100? + 10 Jeopardy Jeopardy
2 Writing Equations Determine whether the data show a linear- relationship. If so, write an equation of a line of fit. Hours, x Battery Life, y 3 7 9 17 26 20 0 86 61 50 ANSWER
2 Writing Equations ANSWER = 6 . 4 + 96 n x Jeopardy
3 Writing Equations The graph shows the distance Lexi can ride her bike in x hours. a) Write an equation of the line b) Interpret the slope c) How long does it take Lexi to ride 30 miles traveling at the same rate? ANSWER
3 Writing Equations ANSWER ?) ? = 10? b) That Lexi travels 10 miles per hour on her bike c) 3 hours Jeopardy
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
4 Writing Eqauations ANSWER ? = 245? 1715 words Jeopardy
5 Writing Equations Gym A charges a fee of $10 per month plus $5 per fitness class. The table shows Gym B s fees. Gym B Fees Number of classes, x 2 5 7 11 Total fee ($) $28 $40 $48 $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
5 Writing Equations ANSWER a. Gym B at $4 per fitness class b. 10 classes Jeopardy
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
1 Line of Fit ANSWER ? = 0.48? + 5.68 ? = 0.93 Strong negative correlation Jeopardy
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? Fruit in a smoothie, x 2 1 4 7 10 3 6 Total cost, y $2.10 $1.50 $3.05 $4.45 $5.95 $1.75 $4.00 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. ANSWER
2 Line of Fit ANSWER The data show a linear relationship ? = 0.5? + 1 About $5.00 Jeopardy
3 Line of Fit The table shows the number of bolts and their mass (in grams) Number of bolts, x 15 12 9 14 22 4 31 Mass (grams), y 61 47 30 59 100 5 140 a) Write an equation of a line of fit for the data. b) Estimate the mass of 20 bolts. ANSWER
3 Line of Fit ANSWER ?) ? = 5.25? 16 b) About 89 grams Jeopardy
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
4 Line of Fit ANSWER No, the correlation coefficient will be close to -1 because the data show a negative correlation. Jeopardy Jeopardy
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
5 Line of Fit ANSWER a) ? = 0.42 + 2.67 b) r = -0.65 The points lie somewhat close to the line. Jeopardy
1 Systems of Equations Name the three options for the solutions to a system of equations ANSWER
1 Systems of Equations ANSWER 1.One solution 2.No solution 3.Infinitely many solutions Jeopardy
2 Systems of Equations Classify the system as consistent or inconsistent. ANSWER
2 Systems of Equations ANSWER Inconsistent The equations are parallel so it has no solutions. Jeopardy
3 Systems of Equations Solve the system 6? + 8? 6? = 62 10? 12? 14? = 14 12? 8? + 20? = 68 ANSWER
3 Systems of Equations ANSWER Exactly one solution (2, 4, -3) Jeopardy
4 Recursive Formulas Solve the system ? + ? + ? = 1 6? + 9? 12? = 14 12? + 18? 24? = 11 ANSWER
4 Systems of Equations ANSWER No solution Jeopardy
5 Recursive Formulas Solve the system 2? 2? + 2? = 12 10? 2? + 10? = 60 2? + 2? + 2? = 12 ANSWER
