FUN 503 Worksheet CRS SKILL FUN 503 Period____________ Name_________________________________________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION FUN 401 Evaluate quadratic functions, expressed in function notation, at integer values. FUN 402 Graph families of functions at integer values Level 2 – MOST students will FUN 503 transformations of quadratic function and attain mastery of the focus skill in absolute value function (vertical translation, isolation. horizontal translation, and vertical stretch) Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will FUN 603 Apply transformations to functions attain mastery of the extension FUN 604 Given an equation or function, find an skill. equation or function whose graph is a translation by a specified amount up or down Level 1 1. Evaluate each of the following functions when a = -­‐5, b = 3, and c = -­‐2. a. f (a, b) = ab − 2b 2 b. f (a, b, c) = a 2 b − 4bc + 3b 2 c. f (a, b, c) =
2. In the function, g(x) = 4( − 3x − 8) + 2 , find the value of the function g, when x = -­‐4. 7a − 3b + 5c
ab
3. Complete the table for the function h(x) = − 2x 3 + 6x 2 − 9 . x h(x) -­‐2 -­‐1 0 1 1 4. Evaluate the function, g(x) = x(2x + 3) , for each given value of x. a. g(0) b. g(−4) 5. Find the value of each function of the given value of x. 1
a. f (x) = x 3 + 2x 2 , find f (3) . 3
b. h(x) =
4.2x − 8.5
, find f (−5) . 3.1x + 5
6. Given the functions f (x) = −2x 2 + 8x −17 and g(x) = 8x 2 − 2x +19 , a. Find f (2) b. Find g(−2) c. Find f (7) − g(−5) 2 7. Complete each table for the function and then graph the function on the grid below. a. b. 2
x x y=
y = x +1 -­‐3 -­‐2 0 1 3 c. x y = (x + 2)
2
-­‐5 -­‐4 -­‐2 -­‐1 0 2 4 -­‐3 -­‐2 0 1 3 x y = x + 2 -­‐8 -­‐4 -­‐3 0 1 2 4 x − 3 d. 3 Level 2 8. Write an equation given the parent function and translation. Problem Parent function Translation Equation 2
a Vertical S
hrink 0
.8 y = x b y = x c y = x 2 d y = x e y = x f y = x 2 g y = x h y = x 2 Down 5 Right 3 Right 8 Vertical Stretch 5 Up 7 Reflected over x-­‐axis Left 7 9. Write the quadratic equation, in vertex form for each graph. a. b. c. d. 4 Level 3 10. Completely describe the transformation of y = x or y = x 2 . a. Left 3, Down 7 y = x 2 b. Right 4, Up 3 y = x c. Reflected over the x-­‐axis, y = x 2 Up 8 2
d. Vertical stretch by a factor y = x of 3, Down 7 e. Right 9, reflected over the y = x x-­‐axis f. Left 7, Down 3 y = x 2 g. Right 8, Vertical stretch by y = x a factor of 5 11. Completely describe the transformation of y = x or y = x 2 . Equation Left/Right Up/Down a) y = x − 2 − 1 b) y = − (X + 3)2 c) y = 2 ( x + 2 ) 2
d) y =
−
x + 2 e) y = − 0.5 X f) y = ( x − 3) + 6 2
REFLECT OF X-­‐
AXIS (YES OR NO) VERTICAL STRETCH OR COMPRESSION 12. Write an equation for each a) Translate y = x right 3 units and up 7 units b) Translate y = x 2 left 8 and down 2 units _____________________ _____________________ 5 13. Write the quadratic equation, in vertex form, for each graph. a. b. c. d. e. f. g. h. 6 Level 4 Graph the quadratic equation on the provided grid. 14. f ( x) = ( x − 0) 2 + 3 15. f ( x) = ( x + 4) 2 + 0 2
16. f ( x) = −2( x − 0) + 0 17. f ( x) = ( x − 3) 2 + 4 1
18. f ( x) = 3( x − 4) 2 − 6 19. f ( x) = ( x + 2) 2 + 3 2
7 Level 5 20. Write the equation of the transformed parent function, f (x) = x , for each graph below. a. b. c. d. Mixed Review 20. Round to the indicated place a. 19,384 to the nearest hundred _____________________ b. 264,980 to the nearest ten thousand __________________ c. 783.0629 to the nearest thousandth ___________________ d. 9.548 to the nearest tenth _____________________ e. 0.395 to the nearest hundredth ________________________ 21. Place the appropriate symbol <, >, or = between the two numbers 8 a. 18 _____ 81 b. 0 _____ -­‐50 c. -­‐3 _____ -­‐5 d. 4.058 _____ 4.06 e. -­‐0.07 _____ -­‐0.007 f. − 6 _____ 6 22. a. Express 42 as a product of prime factors __________________ b. Express 60 as a product of prime factors _________________ c. Find the least common multiple of 42x and 60x 3 _______________ 23. Perform the indicated operations without using a calculator. Simplify your answer, if possible. 1
5
3
2 −5
3
2 3
a. 8 − 4 b. c. d. ( ) 2 − ÷ ÷ 12 •
6
9
5
35 12
5
5 4
9