6B Quiz Review Learning Targets ,

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1 6B Quiz Review Learning Targets , Key Facts Double transformations when more than one transformation is applied to a graph o You can still use our transformation rules to identify which transformations o You must do both transformations to the points on the given graph o In our class, the order of the transformations doesn t matter There are four basic functions and you should know their key points and the shapes of their graphs o y = x o y = x o y = x o y = x When writing function formulas for transformation of our basic graphs, be sure to consider whether you are adding/subtracting/multiplying inside or outside of the function formula f (x) You can use BOTH of your cheat sheets on the quiz! o Transformation rules o Basic graphs Learning Targets 5.10 I can add and subtract matrices, and multiply them by a constant I can use matrices to represent systems of linear equations. 5.1 I can use matrices to solve systems of linear equations with the graphing calculator. 6.1 I can use function notation to answer questions about graphs. 6. Given two graphs, I can identify the transformation of one to the other with a function rules and a written description. 6.3 Given a graph and a transformation (either as a written description or a function rule), I can sketch the resulting graph. 6.4 Given a table and a transformation (either as a written description or a function rule), I can complete the table for the resulting function. 6.5 I can translate between written descriptions, function rules, tables and graphs of transformed functions when there are two or more transformations. 6.6 I can translate between written descriptions, function rules, tables and graphs of transformed functions of the four basic graphs (see above) without a graphing calculator. *This LT is extra credit! 1

2 Practice For problems 1-4, identify the parent function and transformation(s). Then, graph. 1. y = ( 1 x ). y = x + 3. y = x y = x 4

3 For problems 5-7, identify the parent function and transformation(s). Then, write the function formula for the graph Function formula: Function formula: Function formula: 5 For problems 8-1, identify the parent function and transformations. 8. y = x y = 1 3 x 10. y = x+6 3

4 11. y = (x) 8 1. y = 1 5 x Practice 13. The graph of y = f(x) is shown below and to the right. Use it to answer each question. a. If x =, then f(x) = b. If f(x) = 3, then x = c. If x = 1, then f x = d. If x =, then f x = e. If x = 3, then f x 4 = f. If x = 1, then f x = g. If x = 1, then f x = 14. Each graph below is a transformation of y = f(x) (above). Write a description and a function formula for each transformation. a. b. Written Function Formula: Written description: Function Formula: 4

5 15. Given the dotted graph y = f(x) and the function formula, describe the transformation in words, and then graph the transformed function. a. f(x) b. f x c. f(x + ) d. f( x) 5

6 Practice 16. Use the matrices below to answer the following questions. A = B = A B = A = 17. Write a matrix and solve using the rref command on the calculator. Be sure to line up like terms before writing your matrix! y = 3x + 5 4x 3y = Matrix: Reduced Matrix: Solution: x = y = Answers 1. x ; stretch horizontally by a factor of. x ; reflect over x-axis, shift left units 6

7 3. x ; shift right 3 units, shift up 1 unit 4. x ; stretch vertically by a factor of, shift right 4 units 15. a. compressed horizontally by a factor of 5. x ; stretch vertically by a factor of ; x 6. x ; reflect over x-axis, shift left 4 units; x x ; shift right 1 unit, shift down units; (x 1) 8. x ; shift right 4 units, shift up 6 units 9. x ; reflect over y-axis, compress vertically by a factor of x ; reflect over x-axis shift left 6 units 11. x ; compress horizontally by a factor of, shift down 8 units 1. x ; reflect over y-axis, stretch horizontally by a factor of a. 1 b. 3 c. d. 1 e. f. g a. reflected across the y-axis, f( x) b. shifted down units, f x b. shifted down units c. reflected over the x-axis and shifted left units d. Stretched vertically by and reflected over the y-axis Matrix: A B = Reduced Matrix: A = Solution: x = 1 y = 7