Post on 01-Apr-2015
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: