Functions Review

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# Functions Review - PowerPoint PPT Presentation

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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Presentation Transcript
Definitions - 10

Define the domain and range of a function.

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

List all forms (3) of a quadratic function.

• Standard
• Factored
• Vertex
Definitions - 30

In what order should transformations be completed?

• Horizontal reflection and stretch
• Horizontal shift
• Vertical reflection and stretch
• Vertical shift
Definitions - 40

What line is an inverse functions reflected in?

Definitions - 50

List all possible transformations (6) and their

corresponding letter.

• 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

Are the two expressions equivalent?

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

x4- x3 -17x2 +21x+36

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 - 20

Simplify the function and state all restrictions.

-x2 -7x+8 . x +5

x+8 9x-9

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 - 30

Write the function in standard form.

y = 2(x-4)2 -7

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

Simplify the function and state all restrictions.

x+3 ÷ (x-1)(x+3)

x+2 (x-1)2

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 - 50

Simplify the function and state all restrictions.

5 - x _

x2 -5x 5x-25

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

___

State the restrictions of y = √x-4 .

Functions - 20

What is the function for the following graph?

Functions - 30

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

Domain: {x εR}

Range: {y ε R| y ≥ 0}

Functions - 40

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

(-2, -1/2)

(-1, -1)

(-1/2, -2)

(1/2, 2)

(1, 1)

(2, 1/2)

Functions - 50

Write the general form of a transformed function.

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

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

List the transformations on the function.

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

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

Choose any three base points and write them after the

transformation.

______

f(x) = 5√-2(x+1)

(0, 0)  (-1, 0)

(1, 1)  (-1.5, 5)

(4, 2) (-5, 10)

(9, 3)  (-5.5, 15)

(16, 4)  (-9, 20)

Transformations - 40

List all the transformations on the function.

• Shift 4 units right
• Vertical reflection
• Shift 6 units up
Transformations - 50

Write the base function and the transformed function.

Base function: y = 1/x

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

Inverse Functions - 10

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

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

Inverse Functions - 20

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

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

__

What is the inverse of f(x) = 2√-x +3

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

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

________

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

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

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 *