Operations on Functions

Lesson 2.5

ƒ(g(x))

f(x) + g(x)

f(x) - g(x)

f(x) ÷ g(x)f(x) ∙

g(x)

Operations on 1. Rewrite with brackets

around entire .

2. Perform operation on entire quantity.

3. Simplify.

32)( xxf

Find

128 x)(4 xf

[ 𝒇 (𝒙 )]¿ [𝟐 𝒙+𝟑]𝟒 [ 𝒇 (𝒙 )]¿𝟒 [𝟐𝒙+𝟑]

Practice Complete the following problem at your table. Find

ANSWER:

Independent Practice Complete problem set A independently.

Operations on 1. Rewrite with space

instead of x.

2. Substitute input into that space.

3. Simplify.

Find

(__)f 3(__)2

)4( xf 38 x

𝑓 (𝒙 )=2 𝒙+3

𝑓 (𝟒 𝒙)¿2 (𝟒 𝒙 )+3

Practice Complete the following problem at your table. Find

ANSWER:

Independent Practice Complete problem set B independently.

Operations on multiple functions: Adding and Subtracting

Remember to subtract entire quantity (distribute the negative)!

))(( xgf Sometimes written:)()( xgxf Find:

−𝒙𝟐−𝟑 𝒙−𝟏𝟐 𝒙+𝟓()R

Find , fully simplified.

Operations on multiple functions: Multiplying

Practice Complete the following problems

independently.

and . Find .

and . Find .

−𝟐 𝒙+𝟗

−𝟒 𝒙𝟐+𝟏𝟖𝒙−𝟐𝟎

Independent Practice Complete problem set C independently.

Operations on Functions

Lesson 2.5b

ƒ(g(x))

f(x) + g(x)

f(x) - g(x)

f(x) ÷ g(x)f(x) ∙

g(x)

DO NOW Review for the quiz today:

Silently re-read and annotate your notes, HW assignments and classwork. Highlight key points and write down reminders for yourself.

Oral Drill Function or Not?

{(6, -1), (-2, -3), (1,8), (-2,-5)}Not

Function

x Y

a X

b Y

c Y

d Z

Oral Drill Function or Not?

Function

Oral Drill Domain and range of the following relations:

{(6, -1), (-2, -3), (1,8), (-2,-5)} Domain: {6, -2, 1} Range: {-1, -3, 8, -5}

Oral Drill Domain and range of the following relations:

Domain: {a, b, c, d} Range: {X, Y, Z}

x Y

a X

b Y

c Y

d Z

Oral Drill Domain and range of the following relations:

Domain: all real # Range: y 4

Oral Drill If f(x) = 3x+4, what is –f(x)? -f(x) = -3x – 4

If f(x) = 3x+4, what is f(-x)? f(-x) = -3x +4

Oral DrillDescribe the transformations of h(x) =

-horizontal stretch by a factor of -reflection about the y-axis-horizontal translation 3 units to the left-vertical stretch by a factor of 5-reflection about the x-axis-vertical translation 2 units down

Quiz When you finish, organize your binder If you have extra time, please help organize a

partner’s binder

Review

Is the input or output changing? Input – independent variable

Put a space where the original input is!

Substitute the new input.

Review

Is the input or output changing? Output – dependent variable

Write the output, then operate!

Representing Operations Graphically

Use the graph to find f(-2) + g(-2).

Check your work by findingf(x) + g(x) algebraically. Then evaluate for x = -2

)(xf

)(xg

3)4( 1

Representing Operations Graphically

𝑔 (𝑥 )=−𝑥+3

Use the graph to find g(0) x f(0).

g(0) x f(0) 3 -2 -6

Check your work by findingg(x) x f(x) algebraically. Then evaluate for x=0

When x= 0: