1. Functions Review

2. Rational and Equivalent Functions
JEOPARDY!
Definitions
Rational and Equivalent Functions
Functions
Transformations
Inverse Functions 10 20 30 40 50

3. Definitions - 10
Define the domain and range of a function.

4. Definitions – 10 Answer
The domain of a function is the set of all x values that
produce a y value.
The range of a functions is set of all y values that result
from any function.

5. Definitions - 20
List all forms (3) of a quadratic function.

6. Definitions – 20 Answer
Standard
Factored
Vertex

7. Definitions - 30
In what order should transformations be completed?

8. Definitions – 30 Answer Horizontal reflection and stretch
Horizontal shift
Vertical reflection and stretch
Vertical shift

9. Definitions - 40
What line is an inverse functions reflected in?

10. Definitions – 40 Answer
The line y = x

11. Definitions - 50 List all possible transformations (6) and their
corresponding letter.

12. Definitions – 50 Answer k – reflection if k is negative
k – horizontal stretch by a factor of 1/k
p – horizontal shift
a – reflection if a is negative
a – vertical stretch by a factor of a
q – vertical shift

13. Rational and Equivalent Functions - 10
Are the two expressions equivalent?
(x-3)2(x+4)(x+1)
x4- x3 -17x2 +21x+36

14. Rational and Equivalent Functions – 10 Answer
Yes
Solution: Test at least 3 points in both functions to make sure they are they return the
same value.
For example, test x=0
Function 1:
(x-3)2(x+4)(x+1)
=(0-3) 2(0+4)(0+1)
=(-3) 2(4)(1)
=36
Function 2:
x4- x3 -17x2 +21x+36
= (0) 2+21(0)+36

15. Rational and Equivalent Functions - 20
Simplify the function and state all restrictions.
-x2 -7x+8 . x +5
x x-9

16. Rational and Equivalent Functions – 20 Answer
Solution:
-x2 -7x+8 . x +5
x x-9
= -(x-1)(x+8) . x+5
x (x-1)
= -(x+5) 9
-(x+5)
x ≠ -8, 1

17. Rational and Equivalent Functions - 30
Write the function in standard form.
y = 2(x-4)2 -7

18. Rational and Equivalent Functions – 30 Answer
Solution:
y = 2(x-4)2 -7
= 2(x2 -8x+16) -7
= 2x2 -16x+32-7
= 2x2 -16x+25
y = 2x2 -16x + 25

19. Rational and Equivalent Functions - 40
Simplify the function and state all restrictions.
x+3 ÷ (x-1)(x+3)
x (x-1)2

20. Rational and Equivalent Functions – 40 Answer
Solution:
x+3 ÷ (x-1)(x+3)
x (x-1)2
=x (x-1)2__
x (x-1)(x+3)
= x-1
x+2
x - 1
x+ 2
x ≠ -2, 1, -3

21. Rational and Equivalent Functions - 50
Simplify the function and state all restrictions.
x _
x2 -5x x-25

22. Rational and Equivalent Functions – 50 Answer
Solution:
x _
x2 -5x x-25
= x
x(x-5) 5(x-5)
= x x
x(x-5) (x-5) x
= x2
5x(x-5) 5x(x-5)
= x2
5x(x-5)
= - (x2-25)
= -(x+5)(x-5)
= -(x+5) 5x
Find a common denominator: 5x(x-5)
-(x+5) 5x
x ≠ 0, 5

23. Functions - 10
___
State the restrictions of y = √x-4 .

24. Functions – 10 Answer
x ≥ 4

25. Functions - 20
What is the function for the following graph?

26. Functions – 20 Answer _
y = √x

27. Functions - 30
State the domain and range of y = (x+2)2

28. Functions – 30 Answer
Domain: {x ε R}
Range: {y ε R | y ≥ 0}

29. Functions - 40
List all base points of f(x) = 1/x

30. Functions – 40 Answer (-2, -1/2) (-1, -1) (-1/2, -2) (1/2, 2) (1, 1)
(2, 1/2)

31. Functions - 50
Write the general form of a transformed function.

32. Functions – 50 Answer
y = af(k(x-p))+q

33. Transformations - 10
If you start at a point (3, 5) and move 4 units left and 3
units up, what is the new coordinate?

34. Transformations – 10 Answer
(-1, 8)

35. Transformations - 20 List the transformations on the function.
f(x) = -3(x-5)2+1

36. Transformations – 20 Answer
Shift 5 units right
Reflection in the x-axis (vertical reflection)
Vertical stretch by a factor of 3
Shift 1 unit up

37. Transformations - 30
Choose any three base points and write them after the
transformation.
______
f(x) = 5√-2(x+1)

38. Transformations – 30 Answer
(0, 0)  (-1, 0)
(1, 1)  (-1.5, 5)
(4, 2)  (-5, 10)
(9, 3)  (-5.5, 15)
(16, 4)  (-9, 20)
(x, y)
(- x, y)
(- x-1, y)
(-2s+1, 5y)
(0, 0)
(-1, 0)
(1, 1)
(-0.5, 1)
(-1.5, 1)
(-1.5, 5)
(4, 2)
(-4, 2)
(-5, 2)
(-5, 10)
(9, 3)
(-4.5, 3)
(-5.5, 3)
(-5.5, 15)
(16, 4)
(-8, 4)
(-9, 4)
(-9, 20)

39. Transformations - 40
List all the transformations on the function.

40. Transformations – 40 Answer
Shift 4 units right
Vertical reflection
Shift 6 units up

41. Transformations - 50
Write the base function and the transformed function.

42. Transformations – 50 Answer
Base function: y = 1/x
Transformed function: y = - 1/(x+3) -2

43. Inverse Functions - 10
What is the inverse of {(-7, 12), (2, 0), (-10, 4)}.

44. Inverse Functions – 10 Answer
{(0, 2), (4, -10), (12, -7)}

45. Inverse Functions - 20
What is the inverse of y = (1/3 )x +4

46. Inverse Functions – 20 Answer
f -1(x)= 3x-12
Solution:
y = (1/3 )x +4
x = (1/3 )y+4
x-4 = (1/3 )y
3(x-4) =y
f -1 (x) = 3(x-4)
= 3x-12

47. Inverse Functions - 30 __
What is the inverse of f(x) = 2√-x +3

48. Inverse Functions – 30 Answer
f -1(x)= -(1/4)(x – 3)2
Solution:
f(x) = 2√-x +3
y = 2√-x +3
x = 2√-y+3
x-3 = 2√-y
x-3 = √-y 2
x-3 2 = -y
x-3 2 = y
f -1(x) = x-3 2 __ __ __ __ __
( )
-( )
-( )

49. Inverse Functions - 40
What is the inverse of f(x) = 2x2+16x+29

50. Inverse Functions – 40 Answer
________
f -1(x)= 4±√(1/2)(x+3)
Solution:
f(x) = 2x2+16x+29
y = 2x2+16x+29
y = 2(x2+8x) +29
y = 2(x2 +8x ) +29
y = 2(x+4)
y = 2(x+4) 2 -3
x = 2(y+4) 2 -3
X+3 = 2(y+4) 2
X+3 = (y+4) 2 2
X+3 = y+4
X+3 -4 = y __ ±√ __ __ ±√ ±√
f -1 (x) = x+3 2

51. Inverse Functions - 50
Sketch the original and the inverse of the following
function (without finding the inverse). Is the inverse a
function?
f(x) = -(3(x-5))2 -1
HINT - draw the y=x line and then draw the reflection

52. Inverse Functions – 50 Answer
Solution:
Pick at least three
points on the
original function
then use them to
get three points
for the inverse
function.
*Make sure that
sketches are
somewhat
accurate (i.e.
the vertex should
be at the correct
point *