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Functions Review. JEOPARDY!. Definitions - 10. Define the domain and range of a function. 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.

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definitions 10
Definitions - 10

Define the domain and range of a function.

definitions 10 answer
Definitions – 10Answer

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.

definitions 20
Definitions - 20

List all forms (3) of a quadratic function.

definitions 20 answer
Definitions – 20Answer
  • Standard
  • Factored
  • Vertex
definitions 30
Definitions - 30

In what order should transformations be completed?

definitions 30 answer
Definitions – 30Answer
  • Horizontal reflection and stretch
  • Horizontal shift
  • Vertical reflection and stretch
  • Vertical shift
definitions 4 0
Definitions - 40

What line is an inverse functions reflected in?

definitions 50
Definitions - 50

List all possible transformations (6) and their

corresponding letter.

definitions 50 answer
Definitions – 50Answer
  • 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
rational and equivalent functions 10
Rational and Equivalent Functions - 10

Are the two expressions equivalent?

(x-3)2(x+4)(x+1)

x4- x3 -17x2 +21x+36

rational and equivalent functions 10 answer
Rational and Equivalent Functions – 10Answer

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

=04-03-17(0)2+21(0)+36

=36

rational and equivalent functions 2 0
Rational and Equivalent Functions - 20

Simplify the function and state all restrictions.

-x2 -7x+8 . x +5

x+8 9x-9

rational and equivalent functions 20 answer
Rational and Equivalent Functions – 20Answer

Solution:

-x2-7x+8 . x +5

x+8 9x-9

= -(x-1)(x+8) . x+5

x+8 9(x-1)

= -(x+5)

9

-(x+5)

9

x ≠ -8, 1

rational and equivalent functions 3 0
Rational and Equivalent Functions - 30

Write the function in standard form.

y = 2(x-4)2 -7

rational and equivalent functions 30 answer
Rational and Equivalent Functions – 30Answer

Solution:

y = 2(x-4)2 -7

= 2(x2 -8x+16) -7

= 2x2 -16x+32-7

= 2x2 -16x+25

y = 2x2 -16x + 25

rational and equivalent functions 40
Rational and Equivalent Functions - 40

Simplify the function and state all restrictions.

x+3 ÷ (x-1)(x+3)

x+2 (x-1)2

rational and equivalent functions 40 answer
Rational and Equivalent Functions – 40Answer

Solution:

x+3 ÷ (x-1)(x+3)

x+2 (x-1)2

=x+3 . (x-1)2__

x+2 (x-1)(x+3)

= x-1

x+2

x - 1

x+ 2

x ≠ -2, 1, -3

rational and equivalent functions 5 0
Rational and Equivalent Functions - 50

Simplify the function and state all restrictions.

5 - x _

x2 -5x 5x-25

rational and equivalent functions 50 answer
Rational and Equivalent Functions – 50Answer

Solution:

5 - x _

x2-5x 5x-25

= 5 - x

x(x-5) 5(x-5)

= 5 . 5- x . x

x(x-5) 5 5(x-5) x

= 25 - x2

5x(x-5) 5x(x-5)

= 25-x2

5x(x-5)

= - (x2-25)

5x(x-5)

= -(x+5)(x-5)

5x(x-5)

= -(x+5)

5x

Find a common denominator: 5x(x-5)

-(x+5)

5x

x ≠ 0, 5

functions 10
Functions - 10

___

State the restrictions of y = √x-4 .

functions 20
Functions - 20

What is the function for the following graph?

functions 30
Functions - 30

State the domain and range of y = (x+2)2

functions 30 answer
Functions – 30Answer

Domain: {x εR}

Range: {y ε R| y ≥ 0}

functions 40
Functions - 40

List all base points of f(x) = 1/x

functions 40 answer
Functions – 40Answer

(-2, -1/2)

(-1, -1)

(-1/2, -2)

(1/2, 2)

(1, 1)

(2, 1/2)

functions 50
Functions - 50

Write the general form of a transformed function.

functions 50 answer
Functions – 50Answer

y = af(k(x-p))+q

transformations 10
Transformations - 10

If you start at a point (3, 5) and move 4 units left and 3

units up, what is the new coordinate?

transformations 20
Transformations - 20

List the transformations on the function.

f(x) = -3(x-5)2+1

transformations 20 answer
Transformations – 20Answer
  • Shift 5 units right
  • Reflection in the x-axis (vertical reflection)
  • Vertical stretch by a factor of 3
  • Shift 1 unit up
transformations 30
Transformations - 30

Choose any three base points and write them after the

transformation.

______

f(x) = 5√-2(x+1)

transformations 30 answer
Transformations – 30Answer

(0, 0)  (-1, 0)

(1, 1)  (-1.5, 5)

(4, 2) (-5, 10)

(9, 3)  (-5.5, 15)

(16, 4)  (-9, 20)

transformations 40
Transformations - 40

List all the transformations on the function.

transformations 40 answer
Transformations – 40Answer
  • Shift 4 units right
  • Vertical reflection
  • Shift 6 units up
transformations 50
Transformations - 50

Write the base function and the transformed function.

transformations 50 answer
Transformations – 50Answer

Base function: y = 1/x

Transformed function: y = - 1/(x+3) -2

inverse functions 10
Inverse Functions - 10

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

inverse functions 10 answer
Inverse Functions – 10Answer

{(0, 2), (4, -10), (12, -7)}

inverse functions 20
Inverse Functions - 20

What is the inverse of y = (1/3 )x +4

inverse functions 20 answer
Inverse Functions – 20Answer

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

inverse functions 30
Inverse Functions - 30

__

What is the inverse of f(x) = 2√-x +3

inverse functions 30 answer
Inverse Functions – 30Answer

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-32 = -y

2

x-32 = y

2

f-1(x) = x-32

2

__

__

__

__

__

( )

-( )

-( )

inverse functions 40
Inverse Functions - 40

What is the inverse of f(x) = 2x2+16x+29

inverse functions 40 answer
Inverse Functions – 40Answer

________

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 +16-16) +29

y = 2(x+4) 2 -32+29

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

2

X+3 -4 = y

2

__

±√

__

__

±√

±√

f -1 (x) =-4 x+3

2

inverse functions 50
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

inverse functions 50 answer
Inverse Functions – 50Answer

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 *