Math Substituting the Function Notation

Evaluating Functions

To EVALUATE a Function is to: Replace (substitute) its variable with a given number or expression

Function Notation

f(x)

We call this "f of x"

f is the function name and x is the input

f(x) is the output

Input: what gets plugged in

Output: the answer for the given input

Key Words

• Evaluate: to determine the value of something

• Function: a relation in which each element of the domain is mapped to (paired with) exactly one element of the range

• Input: the value that is transformed by a process and becomes an output

• Output: The result of an input that has been transformed by a process

​The number in the parenthesis, 3, is the x value and f(3) is the y value!

​If we were evaluating a function and got

​what would this be as an ordered pair?

Multiple Choice

Does this mapping diagram represent a function?

• No, because there are repeating input values

• Yes, because there are no repeating input values

Multiple Choice

$$f\left(x\right)=x^2-9x+2$$   Evaluate:  $$f\left(-2\right)$$  

• $$f\left(-2\right)=24$$  

• $$f\left(-2\right)=-20$$  

• $$f\left(-2\right)=16$$  

• $$f\left(-2\right)=-12$$  

Multiple Choice

f(x)=4x+5

f(4)=

• 21

• -11

• -31

• 25

Multiple Choice

If f(x) = 2x² + 5x - 3, evaluate f(-1).

• f(-1) = -6

• f(-1) = 1

• f(-1) = -10

• f(-1) = -1

Evaluating from a graph

• Evaluate for f(5)

• Find where the function has an x-value of 5

• The y-value of that point is your answer

• f(5)=2

​When we are evaluating functions from graphs, we want to pay attention to what the y-value is for the given x value, which we find in parentheses

​Now, let's find !

Multiple Choice

With this in mind, try to find  $$f\left(4\right)$$  from this graph, 

• 4

• -5

• -6

• 1

Multiple Choice

Use the graph to find  $$f\left(1\right)$$  

• 6

• 5

• -7

• 0

Multiple Choice

Use the graph to find  $$f\left(0\right)$$  

• 6

• 5

• -7

• 0

What if we were asked to find x when f(x)=-5

​x = 4

Multiple Choice

Use the graph to find  $$x$$  when  $$f\left(x\right)=-2$$  

• 6

• 5

• -7

• 0

Multiple Choice

Given the function table: determine h(-1)

• -8

• 1

• -5

• 2

Multiple Choice

Given the function table: determine h(2)

• -5

• 1

• -2

• -8

Multiple Choice

Given the function table: what is t if h(t) = -5

• -1

• 1

• 0

• 2

Multiple Choice

Given the function table: determine f(1)

• -4

• 5

• 8

• 11

Multiple Choice

Given the function table: determine f(-2)

• -4

• 5

• 8

• 11

Multiple Choice

Given the function table: what is x if f(x) = 11

• 1

• 2

• 3

• 11

Multiple Choice

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

• Let x = 2

• Let y = 2

Multiple Choice

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

• 6

• 7

• 8

• 9

Multiple Choice

$$f\left(1.5\right)=?$$  

• 0

• 2

• 6

• -1

Multiple Choice

Evaluate for f(1)

• 0

• -3

• 3

• 2

Multiple Choice

Evaluate for f(-5)

• 1

• 0

• 2

• -2

Multiple Choice

Given that h(x)=x³-2, evaluate h(4)

• 62

• 10

• 64

• 12