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2.4 – Operations with Functions. Objectives: Perform operations with functions to write new functions Find the composition of two functions Standard: 2.8.11.S. Analyze properties and relationships of functions. I. Operations With Functions. For all functions f and g : - PowerPoint PPT Presentation

### Transcript of 2.4 – Operations with Functions

• 2.4 Operations with Functions

Objectives: Perform operations with functions to write new functionsFind the composition of two functionsStandard: 2.8.11.S. Analyze properties and relationships of functions

• I. Operations With FunctionsFor all functions f and g:

Sum (f + g)(x) = f(x) + g(x)

Difference (f g)(x) = f(x) g(x)

Product (f g)(x) = f(x) g(x)

Quotient ( )(x) = , where g(x) 0

• Example

• Solve the following:

• ExampleState any domain restrictions.

• Example 4

• Composition of FunctionsLet f and g be functions of x.

The composition of f and g, denoted f g, is defined by f(g(x)).

The domain of y = f(g(x)) is the set of domain values of g whose range values are the domain of f. The function f g is called the composite function of f with g.

• Example

• Example 2

• Example 4

• Example 5A local computer store is offering a \$40.00 rebate along with a 20% discount. Let x represent the original price of an item in the store.a. Write the function D that represents the sale price after a 20% discount and the function R that represents the sale price after the \$40 rebate.b. Find the composition functions (R D)(x) and (D R)(x), and explain what they represent.

Since the 20% discount on the original price is the same as paying 80% of the original price, D(x) = 0.8x The rebate function is R(x) = x - 4020% discount first\$40 rebate firstR(D(x)) = R(0.8x)D(R(x)) = D(x 40) = (0.8x) 40 = 0.8(x 40) = 0.8x 40 = 0.8x 32 Notice that taking the 20% discount first results in a lower sales price.

• Writing Activities5. What is the difference between (fg)(x) and (f g)(x)? Include examples to illustrate your discussion.

6. In general, are (f g)(x) and (g f)(x) equivalent functions? Explain.

• Homework

Integrated Algebra II- Section 2.4 Level A

Honors Algebra II- Section 2.4 Level B

• End Section 2.4

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