1. 3.3 Function notation
Students will be able to: use the function notation to solve and graph functions.

2. Equations in function notation
F(x)
A linear equation written in the form of y = mx + b can be written as f(x) = mx + b in function notation.
Examples:
y = 2x –  f(x) = 2x – 3
y = ¼ n + 6  f(n) = ¼ n + 6
y = x2 – 8  f(x) = x2 – 8
y = -2m + 1  f(m) = -2m + 1

3. Evaluating functions
Example: Evaluate f(x) = 2x + 6 when x = 1, 0, and -1
Plug in each value of x.
f(1) = 2(1) + 6
f(1) = 2 + 6
f(1) = 8
Answer (1, 8)
b) f(0) = 2(0) + 6
f(0) = 0 + 6
f(0) = 6
Answer (0, 6)
c) f(-1) = 2(-1) + 6
f(-1) =
f(-1) = 4
Answer (-1, 4)

4. Evaluating functions
You try: Evaluate g(n) = -4n + 7 when n = 2, 0, and -2
Plug in each value of n.
g(2) = -4(2) + 7
g(2) =
g(2) = -1
Answer (2, -1)
b) g(0) = -4(0) + 7
g(0) = 0 + 7
g(0) = 7
Answer (0, 7)
c) g(-2) = -4(-2) + 7
g(-2) = 8 + 7
g(-2) = 15
Answer (-2, 15)

5. Interpreting function notation
Example: Let f(t) be the outside temperature (oF) t hours after 6 a.m. Explain the meaning of each statement.
f(0) = 58
f(6) = n
f(3) < f(9)
Solution
t=0 which is 0 hours after 6 a.m. so the temperature at 6 a.m. is 58 degrees
t=6 which is 6 hours after 6 a.m. so the temperature at 12 pm is n degrees
t=3 is 3 hours after 6 a.m. and t=9 is 9 hours after 6 am, so the temperature at 9 a.m. is less than the temperature at 3 p.m.

6. Interpreting function notation
You try: Let f(t) be the outside temperature (oF) t hours after 9 a.m. Explain the meaning of each statement.
f(2) = f(9)
F(m) = 70
f(6) > f(0)
Solution
T = 2 is 2 hours after 9 a.m. and t = 9 is 9 hours after 9 a.m. So, the temperature at 11 a.m. is the same as the temperature at 6 p.m.
t = m is m hours after 9 a.m. So, the temperature in m hours after 9 a.m. is 70 degrees.
t = 6 is 6 hours after 9 a.m. and t = 0 is 0 hours after 9 a.m. So, the temperature at 3 p.m. is greater than the temperature at 9 a.m.

7. Using function notation
Examples: Find the value of x so that the function has the given value.
1. h(x) = 2 3 x – 5 when h(x) = -7
-7 = 2 3 x – 5
-2 = 2 3 x
-6 = 2x
-3 = x 1
(3)
(3) 1

8. Using function notation
You try: Find the value of x so that the function has the given value.
1. g(x) = 1 3 x – 2 when g(x) = -4
-4 = 1 3 x – 2
-2 = 1 3 x
-6 = x 1
(3)
(3)

9. Graphing a linear function in function notation
Graph f(x) = 2x + 5
a) make a table b) Plot the ordered pairs
X f(x)= 2x f(x) (x,f(x)) -2 -1
012
f(-2) = 2(-2) + 5
F(-1) = 2 (-1) +5
f(0) = 2(0) + 5
f(1) = 2(1) + 5
f(2) = 2(2) + 5 1 3 5 7 9
(-2, 1)
(-1, 3)
(0,5)
(1,7)
(2,9)

10. Graphing a linear function in function notation
Graph f(x) = 3𝑥−2
a) make a table b) Plot the ordered pairs
X f(x)= 3𝑥− f(x) (x,f(x)) -2 -1
012
𝑓(−2) = 3(−2) −2
𝑓(−1) = 3(−1) −2
𝑓(0) = 3(0) −2
𝑓(1) = 3(1) −2
𝑓(2) = 3(2) −2 -8 -5 -2 1 4
(-2, -8)
(-1, -5)
(0,-2)
(1,1)
(2,4)