Function Notation and Evaluating Functions

Evaluating Functions

by Dana Cook

​What is a function and its notation?

​1. A function is a special relation in math where each ________ goes with

​ ___________ _____ __________.

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​2. We use ___________ ___________ as a quick way to

​ _____________ functions.

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​3. Instead of writing _________, we write _______________.

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​4. IMPORTANT: f(x) does _______ mean _________ ____________!!

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Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE output
• Inputs have different outputs every time
• x-values and y-values

Multiple Choice

How do you read f(x)?

• f times x

• f of x

• f parenthesis x

• f with an x inside parenthesis

Multiple Choice

What is function notation?

• adding functions.

• i wasn't listening

• the way an equation (function) is written.

• pass.

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

​Be careful...Make sure you notice the difference in these notations!

​f(3)

​Means find the value of the function f when x = 3. In other words, plug in ________ and calculate to find the answer.

​

​Example:

​Given f(x) = 2x + 1

​

​find f(3) ___________

​f(x) = 3

​Means that the whole function is equal to 3. In other words, replace f(x) with _______ and ________ for x.

​

​Example:

​

​Given f(x) = 2x + 1 and f(x) = 3, find x.

​Skill 1: Evaluating from function notation.

​1) f(x) = 3x - 4, find.......

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​a) f(-1) b) f(6) c) f(-2)

​You Try.....

​2) If g(x) = -6x + 1, find ....

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a) g(0) b) g(-4) c) g(3)

Multiple Choice

What is f(6) for the function f(x)=3x-8

• -8

• 10

• -144

• answer not here

Multiple Choice

What is  $$f\left(0\right)$$   for the function $$f\left(x\right)=2x+3$$  

• 2x

• -3

• 3

• 10

Multiple Choice

If f(x) = 5x - 12, then what is f(-4)?

• -32

• -3

• -12

• 3

Multiple Choice

If f(x) = 2x + 1, what would the function look like

once you substitute in a 1 to find f(1)?

• f(x) = 21+1

• f(1) = 2 (1) + 1

• f(1) = 2x (1) + 1

Multiple Choice

What is f(−4) for the function f?

f(x) = 2x + 3

• -5

• -4

• -2

• -7

Multiple Choice

What is f(5) for the function f?

f(x) = 2(x - 7)

• 3

• -4

• -3

• 1

​​Skill 2: Evaluating from a table.

​Examples:

​

​

​a) f(-7) b) f(15) c) If f(x) = 5, what is x?

​You try.....

​

​

​a) f(4) b) IF f(x) = 2, what is x? c) If f(x) = 0, what is x?

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Evaluate f(5)

• 1
• 10
• 13
• 16

Multiple Choice

Determine the value of x given f(x) = 10

• 33

• 11

• 10

• 30

Multiple Choice

Fill in the blank:  $$f\left(-1\right)=$$  _____

• -2

• 1

• 4

• 7

Multiple Choice

Find the value of x where f(x) = 2

• 0

• 1

• 2

• 3

​Using function notation to find x.

​1) Let f(x) = 4x - 6, find x if .....

​

​a) f(x) = 4 b) f(x) = -1 c) f(x) = 0

​Using function notation to find x.

​2) Let g(x) = 3x - 1, find x if .....

​

​a) g(x) = -10 b) g(x) = 2. c) g(x) = 0

Multiple Choice

If f(x)=2x+2 and f(x)= 2

then what is the value of x?

• 6

• -8

• 10

• 0

Multiple Choice

If f(x)=x+3 and f(x) = -5,

then what is the value of x?

• -2
• -1
• -8
• 7

Multiple Choice

If f(x)=-x+3 and f(x) = 7,

then what is the value of x?

• -4
• -6
• 3
• 13

Multiple Choice

g(x) = 11 - x
Find g(x) = -7 

• 4
• 17
• 18
• -77

Multiple Choice

If g(x) = 5 - 6x, then find g(-5)

• g(-5) = -25
• g(-5) = 6
• g(-5) = 4
• g(-5) = 35

​Function Notation with Graphs

​1) Use the Graph to find the following:

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​a) f(-2) b) f(4)

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​

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​c) when f(x) = 4 x = _______

​Function Notation with Graphs

​2) Use the graph to find the following:

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​a) f(-4) b) f(1)

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​

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​c) when f(x) = -3 x = _______

​Practice

​3) Use the graph of d(t) to find the following.

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​a) d(2) b) d(4)

​

​

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c) when d(t) = 4, t = ______

​Practice

​4) Use the graph of d(t) to find the following.

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​a) d(9) b) d(6)

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​

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c) when d(t) = 2, t = ______