Foundations U7L4 Lesson

Functions

Remember, a function Is like a machine ...

• It has an input.

• It has an output.

• It has a rule that is applied to the input to produce the output.

• Each input has one and only one "guaranteed" output.

• In other words, if you know the input, you "know" the output.

Multiple Select

Which of the following is a function? [Select ALL that apply]

Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE guaranteed output

• Inputs have different outputs every time
• x-values and y-values

Drag and Drop

A function can be thought of as a ​

Placeholder

that assigns one ​

Placeholder

to every ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

machine

output

input

Multiple Choice

Is the relation a function? Why.

• Yes, because the input value 11 has two output values paired with it.

• Yes, because each input value has only one output value paired with it.

• No, because the input value 11 has two output values paired with it.

• No, because each input value has only one output value paired with it.

Multiple Choice

Does the table represent a function?

• Yes, there  is a repeated input value. 

• No, there aren't any repeated output values.

• Yes, there are repeated output values. 

• No, there is a repeated input value. 

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

​is a FUNCTION because each input has a "guaranteed" output.

In this EQUATION, the input is x and the output is y.

​For this function, suppose the input, x, is 5. The output, y, will be 15 using the function machine method..

​Another way to find the output of a function is to use SUBSTITUTION. Substitution means to plug in the given input value into the equation for the x using ( ).

​y = 3x
y = 3(5)
y = 15

Multiple Choice

Find the output.

• 17

• 55

• 30

• 37

Multiple Choice

Given the function, y = 2x - 5. What is the y also known as?

• Output

• Input

• Rule

Multiple Choice

Given the function, y = 2x - 5. What is the x also known as?

• Output

• Input

• Rule

Function Notation

• A specific way to write a rule when it is a function. ​

• General Function Notation: f(x)

• Said out loud: "f of x"

​

Example:

y = 2x + 1 is a function.

So it can also be written as f(x) = 2x + 1.

Multiple Choice

f(x) means the same thing as ____.

• x

• t

• y

• r

Multiple Choice

How would you write y = 2x - 3 in function notation?

• y = 2x - 3

• f = 2x - 3

• f(x) = 2x -3

Why Use Function Notation?

1. Function Notation tells us the NAME of the function and the INPUT VARIABLE.
   
   
   For the function f(x) = 2x + 1, the function's NAME is f and the INPUT VARIABLE is x.1.

Drag and Drop

In the function, g(a) = 2a + 1, the g is the ​

Placeholder

of the function and the (a) identified the ​

Placeholder

of the function.

Drag these tiles and drop them in the correct blank above

name

input variable

Multiple Choice

Which statement best describes the function h(t) = 210 – 15t?

• h is the function name; h(t) is the input variable; and t is the output variable.

• h is the function name; t is the input variable; and h(t) is the output variable.

• t is the function name; h(t) is the input variable; and h is the output variable.

• t is the function name; h is the input variable; and h(t) is the output variable.

Labelling

Identify the parts:

Drag labels to their correct position on the image

This is the input variable

This is the name of the function.

This is what the function does.

Why Use Function Notation?

2. Function NOTATION clearly identifies the value of the input.

   For the function f(x) = 2x + 1, find f(5) means the input value is 5.

Match

Match the following

• f(5)

• g(2)

• h(-3)

• k(17)

• m(12)

the function's input value is 5

the function's input value is 2

the function's input value is -3

the function's input value is 17

the function's input value is 12

• the function's input value is 5

• the function's input value is 2

• the function's input value is -3

• the function's input value is 17

• the function's input value is 12

Evaluating Functions

The question we answered

Given y = 2x + 1, find the value of y when x = 5.

​

Can be asked this way using function notation.

Given f(x) = 2x + 1, find f(5).

Function Machine

You will also see this type of function machine.

You can see that x is being put into the machine, and f(x), which is the output, is coming out.

Multiple Choice

Let's Try it:

If the input is -3, determine the corresponding output.

• f(-3) = -2

• f(-3) = 10

Example 1

Here, we're told that our rule is

f(x) = -2x +4 and that x is equal to -3.

When we input -3 into our equation, we get an output of 10.

Make sure you are using FUNCTION NOTATION. f(-3) = 10. This is read f of -3 equal 10.

How to Evaluate

• Given the function h

• Substitute 3, a domain value, on both sides of = for k

• Use order of operations (PEMDAS) to simplify

Multiple Choice

Find f(x) if x=-2.

• f(x)=9

• f(x)=-15

• f(x)=-9

• f(x)=21

Multiple Choice

Given: $$g\left(x\right)=x^2-3x+1$$  . Find $$g\left(-5\right)$$  .

• $$-41$$  

• $$-9$$  

• $$41$$  

• $$9$$  

Multiple Choice

f(5) = ?

• 25

• 125

• 5

• 10

Multiple Choice

• 16

• 48

• -28

• 4

Multiple Choice

Evaluate $$g\left(a\right)=-2a-5$$  at $$a=4$$  

• g(4)=13

• g(4)=3

• g(4)=-13

• g(4)=4

Multiple Choice

f(x) is the same thing as ______.

• y

• x

• input

• an equation

Multiple Choice

If a question asks you to find f(2), what does that mean?

• Let x = 2

• Let y = 2

Multiple Choice

If f(x) = 2x + 1, what would be your first step to find f(1)?

• Plug a 1 in for all the x's using ( ).

• Set the function equal to 1.

• Multiply the rule by 1.

• Only plug a 1 into the left side.

Multiple Choice

If f(x) = 2x + 1, find f(1).

• f(1) = 1

• f(1) = 4

• f(1) = 2x + 1

• f(1) = 3

Multiple Choice

If f(x) = 6x - 9, find f(4).

• (4, 1)

• (4, 33)

• (4, 15)

• (4, -7)

Multiple Choice

g(x) = 3x + 1
g(2) = _______

• 6

• 7

• 8

• 9