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**Operations on Functions**

f(x) + g(x) f(x) β g(x) f(x) Γ· g(x) f(x) - g(x) Ζ(g(x)) Operations on Functions Lesson 2.5

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**Operations on π(π) Find ππ(π) [π π ] =[ππ+π] π[π π ] =π[ππ+π]**

Rewrite with brackets around entire π(π). Perform operation on entire quantity. Simplify. Find ππ(π) [π π ] =[ππ+π] π[π π ] =π[ππ+π] Which variable is 4 being added to? What do I mean when I say βentire dependent variableβ?

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**Practice Complete the following problem at your table.**

π π₯ = 1 2 π₯β2 Find 6π π₯ β8 ANSWER: 6π π₯ β8=3π₯β20

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Independent Practice Complete problem set A independently.

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**π π =2π+3 π(ππ) =2 ππ +3 Operations on π₯ Find π(ππ)**

Rewrite with space instead of x. Substitute input into that space. Simplify. π π =2π+3 Find π(ππ) π(ππ) =2 ππ +3 Which variable is 4 being added to? What will we substitute in for parentheses?

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**Practice Complete the following problem at your table.**

π π₯ = 1 2 π₯β2 Find π(6π₯β8) ANSWER: π 6π₯β8 =3π₯β6

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Independent Practice Complete problem set B independently.

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**Operations on multiple functions: Adding and Subtracting**

Find: Sometimes written: ππ+π β π π βππβπ ( ) What is being subtracted from 2x+5? If they say g(x), say what is g(x)? How do I write that I am subtracting π₯ 2 β3π₯β1? R Remember to subtract entire quantity (distribute the negative)!

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**Operations on multiple functions: Multiplying**

Find (πβπ)(π₯), fully simplified.

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**Practice Complete the following problems independently.**

π π₯ =2π₯β4 and β π₯ =β2π₯+5. Find (ββπ)(π₯). π π₯ =2π₯β4 and β π₯ =β2π₯+5. Find (πββ)(π₯). βππ+π βπ π π +πππβππ

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Independent Practice Complete problem set C independently.

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**Operations on Functions**

f(x) + g(x) f(x) β g(x) f(x) Γ· g(x) f(x) - g(x) Ζ(g(x)) Operations on Functions Lesson 2.5b

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**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.

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**Oral Drill Function or Not? {(6, -1), (-2, -3), (1,8), (-2,-5)} Not**

x Y a X b c d Z

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Oral Drill Function or Not? Function

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**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}

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**Oral Drill Domain and range of the following relations:**

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

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**Oral Drill Domain and range of the following relations:**

Domain: all real # Range: y β€4

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

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Oral Drill Describe the transformations of h(x) = β5 β 1 3 π₯+3 β2 -horizontal stretch by a factor of 1 3 -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

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**Quiz When you finish, organize your binder**

If you have extra time, please help organize a partnerβs binder

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**Review π π₯ =3π₯β5. πΉπππ βπ π₯ Is the input or output changing?**

Input β independent variable Put a space where the original input is! π =3 β5 Substitute the new input. π π₯+1 =3 π₯+1 β5 =3π₯+3 β5 =3π₯ β2

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**Review π π₯ =3π₯β5. πΉπππ π π₯+1 Is the input or output changing?**

Output β dependent variable Write the output, then operate! π π₯ =3π₯β5 βπ π₯ =β 3π₯β5 βπ π₯ =β3π₯+5

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**Representing Operations Graphically**

Use the graph to find f(-2) + g(-2). Check your work by finding f(x) + g(x) algebraically. Then evaluate for x = -2 οΌ TIME PERMITTING οΌ

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**Representing Operations Graphically**

π π₯ =π₯β2 π π₯ =βπ₯+3 Use the graph to find g(0) x f(0). g(0) x f(0) 3 Γ -2 -6 Check your work by finding g(x) x f(x) algebraically. Then evaluate for x=0 (π₯β2)(βπ₯+3) βπ₯ 2 +5π₯β6 When x= 0: β β6 β6

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Drill Solve the linear system by substitution. 1.y = 6x β 11 -2x β 3y = -7 2.-4x + y = 6 -5x β y = 21.

Drill Solve the linear system by substitution. 1.y = 6x β 11 -2x β 3y = -7 2.-4x + y = 6 -5x β y = 21.

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