Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its

IntroductionSo far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its domain. But, can a function be applied to expressions other than x? What would it mean if we wrote f(2x) or f(x + 1)? In this lesson, we will explore function notation and the versatility of functions.

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3.1.4: Function Notation and Evaluating Functions

Introduction, continuedFor example, let f be a function with the domain {1, 2, 3} and let f(x) = 2x. To evaluate f over the domain {1, 2, 3}, we would write the following equations by substituting each value in the domain for x:

f(1) = 2(1) = 2

f(2) = 2(2) = 4

f(3) = 2(3) = 6

{2, 4, 6} is the range of f(x).

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Key Concepts• Functions can be evaluated at values and variables.

• To evaluate a function, substitute the values for the domain for all occurrences of x.

• To evaluate f(2) in f(x) = x + 1, replace all x’s with 2 and simplify: f(2) = (2) + 1 = 3. This means that f(2) = 3.

• (x, (f(x)) is an ordered pair of a function and a point on the graph of the function.

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Common Errors/Misconceptions• thinking function notation means “f times x” instead of

“f of x”

• trying to multiply the left side of the function notation

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Guided Practice

Example 1Evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}. What is the range?

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Guided Practice: Example 1, continued

1. To evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}, substitute the values from the domain into f(x) = 4x – 7.

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2. Evaluate f(1).

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f(x) = 4x – 7 Original function

f(1) = 4(1) – 7 Substitute 1 for x.

f(1) = 4 – 7 = –3 Simplify.


3. Evaluate f(2).

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f(2) = 8 – 7 = 1 Simplify.


4. Evaluate f(3).

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f(3) = 12 – 7 = 5 Simplify.


5. Evaluate f(4).

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f(4) = 16 – 7 = 9 Simplify.


6. Collect the set of outputs from the inputs.

The range is {–3, 1, 5, 9}.

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http://walch.com/ei/CAU3L1S4EvalFunc1

Guided Practice

Example 3Raven started an online petition calling for more vegan options in the school cafeteria. So far, the number of signatures has doubled every day. She started with 32 signatures on the first day. Raven’s petition can be modeled by the function f(x) = 32(2)x. Evaluate f(3) and interpret the results in terms of the petition.

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1. Evaluate the function.

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f(x) = 32(2)x Original function

f(3) = 32(2)3 Substitute 3 for x.

f(3) = 32(8) Simplify as needed.

f(3) = 256


2. Interpret the results. On day 3, the petition has 256 signatures. This is a point on the graph, (3, 256), of the function f(x) = 32(2)x.

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Days

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http://walch.com/ei/CAU3L1S4EvalFunc2

Documents

Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its