1. How can you use function notation to represent a function?
3.3
Function Notation
How can you use function notation to represent a function?
Students will be able to use function notation to evaluate and interpret functions.
Students will be able to use function notation to solve and graph functions.

2. Students will be able to use function notation to evaluate and interpret functions.
You know that a linear function can be written in the form 𝑦=𝑚𝑥+𝑏. By naming a linear function f, you can also write the function using function notation.
𝑓 𝑥 =𝑚𝑥+𝑏 this is function notation
The notation 𝑓(𝑥) is another name for y. Remember 𝑦=𝑓(𝑥)
Remember x is the input and 𝑓(𝑥) is the output.
You can use letters other than f to name a function, such as g or h.

3. Students will be able to use function notation to evaluate and interpret functions.
Evaluate 𝑓 𝑥 =−4𝑥+7 when 𝑥=2 and 𝑥=−2.
𝑓 𝑥 =−4𝑥+7
𝑓 2 =−4(2)+7
=−8+7
=−1
𝑓(2)=−1
When 𝑥=2, 𝑓(𝑥)=−1
𝑓 𝑥 =−4𝑥+7
𝑓 −2 =−4(−2)+7
=8+7
=15
𝑓(−2)=15
When 𝑥=−2, 𝑓(𝑥)=15

4. You try!!
Students will be able to use function notation to evaluate and interpret functions.
Evaluate 𝑓 𝑥 =2𝑥−5 when 𝑥=−4, 0, 𝑎𝑛𝑑 3.
𝑓 −4 =2 −4 −5
=−8−5
=−13
𝑓(−4)=−13
When 𝑥=−4, 𝑓(𝑥)=−13
(−4,−13)
𝑓 0 =2 0 −5
=0−5
=−5
𝑓(0)=−5
When 𝑥=0, 𝑓(𝑥)=−5
(0,−5)
𝑓 3 =2 3 −5
=6−5 =1
𝑓(3)=1
When 𝑥=3, 𝑓(𝑥)=1
(3,1)

5. You try!!
Students will be able to use function notation to evaluate and interpret functions.
Evaluate g 𝑥 =−𝑥−1 when 𝑥=−4, 0, 𝑎𝑛𝑑 3.
g −4 =− −4 −1
=4−1 =3
𝑔(−4)=3
(−4,3)
g 0 =− 0 −1
=0−1
=−1
𝑔(0)=−1
(0,−1)
g 3 =− 3 −1
=−3−1
=−4
𝑔 3 =−4
(3,−4)

6. Students will be able to use function notation to evaluate and interpret functions.
Let ℎ(𝑡) be the outside temperature ℉ 𝑡 hours after 6 A.M. Explain the meaning of each statement.
ℎ(0)=58
ℎ 6 =𝑛
ℎ 3 <ℎ(9)
The initial value of the function is 58.
So, the temperature at 6 A.M. is 58℉.
The output of h when 𝑡=6 is n.
So, the temperature at noon (6 hours after 6 A.M.) is 𝑛℉.
The output of h when 𝑡=3 is less than the output of h when 𝑡=9.
So, the temperature at 9 A.M. (3 hours after 6 A.M.) is less then the temperature at 3 P.M. (9 hours after 6 A.M.)

7. You Try!!
Students will be able to use function notation to evaluate and interpret functions.
Let 𝑔(𝑡) be the outside temperature ℉ 𝑡 hours after 9 A.M. Explain the meaning of each statement.
𝑔(4)=75
𝑔 𝑚 =70
𝑔 2 =𝑔(9)
The output of g when 𝑡=4 is 75.
So, the temperature at 1 P.M. (4 hours after 9 A.M.) is 75℉.
The output of g when 𝑡=𝑚 is 70.
So, the temperature 𝑚 hours after 9 A.M. is 70℉.
The output of g when 𝑡=2 equals the output of g when 𝑡=9.
So, the temperature at 11 A.M. (2 hours after 9 A.M.) equals the temperature at 6 P.M. (9 hours after 9 A.M.)

8. 2. Students will be able to use function notation to solve and graph functions.
For ℎ 𝑥 = 2 3 𝑥−5, find the value of x for which ℎ 𝑥 =−7.
ℎ 𝑥 = 2 3 𝑥−5
−7= 2 3 𝑥−5
−2= 2 3 𝑥
−2= 2 3 𝑥
3 2 ∙−2= 3 2 ∙ 2 3 𝑥
−3=𝑥
When 𝑥=−3, ℎ 𝑥 =−7.
ℎ −3 =−7

9. You Try!!
2. Students will be able to use function notation to solve and graph functions.
For 𝑔 𝑥 =− 1 2 𝑥+3, find the value of x for which 𝑔 𝑥 =−1.
𝑔 𝑥 =− 1 2 𝑥+3
−1=− 1 2 𝑥+3
−4=− 1 2 𝑥
−4=− 1 2 𝑥
(−4)(−2)=(− 1 2 𝑥)(−2)
8=𝑥
When 𝑥=8, 𝑔 𝑥 =−1.
𝑔 8 =−1

10. Make an input-output table to find ordered pairs.
2. Students will be able to use function notation to solve and graph functions.
Graph 𝑓 𝑥 =2𝑥+5.
Make an input-output table to find ordered pairs. x -2 -1 1 2
f(x) 3 5 x -2 -1 1 2
f(x) 3 5 7 x -2 -1 1 2
f(x) 3 5 7 9 x -2 -1 1 2
f(x) x -2 -1 1 2
f(x) 3 x -2 -1 1 2
f(x)
We call these numbers the fab five: -2, -1, 0, 1, 2
Plot the ordered pairs.
Draw a line through the points.

11. Make an input-output table to find ordered pairs.
You Try!!
2. Students will be able to use function notation to solve and graph functions.
Graph 𝑓 𝑥 =−𝑥+4.
Make an input-output table to find ordered pairs. x -2 -1 1 2
f(x) 6 5 4 x -2 -1 1 2
f(x) 6 5 x -2 -1 1 2
f(x) 6 5 4 3 x -2 -1 1 2
f(x) 6 5 4 3 x -2 -1 1 2
f(x) 6 x -2 -1 1 2
f(x)
We call these numbers the fab five: -2, -1, 0, 1, 2
Plot the ordered pairs.
Draw a line through the points.

12. So let’s review!
What have we covered so far?
Students will be able to use function notation to evaluate and interpret functions.
How do we evaluate? Find 𝑓 𝑥 =−2𝑥−7 when 𝑥=3
Plug it in! Plug it in!
𝑓 3 =−2 3 −7=−13
How do we interpret? 𝑓 𝑡 =4𝑡−12, t is hours and 𝑓(𝑡) is miles
What does the value of the function mean? 𝑓 5 =300
After 5 hours we have traveled 300 miles.

13. What have we covered so far? Continued
So let’s review!
What have we covered so far? Continued
Students will be able to use function notation to solve and graph functions.
How do we solve? Find x when 𝑓 𝑥 =−6 if 𝑓 𝑥 = 3 2 𝑥−5
Set the equation equal to the value and solve for the variable.
−6= 3 2 𝑥−5
𝑥=− 2 3
How do we graph?
Plug in the fab five and plot on a graph x -2 -1 1 2
f(x)