1. Chapter 3
Section 6

2. Function Notation and Linear Functions
3.6
Function Notation and Linear Functions
Use function notation.
Graph linear and constant functions.

3. Objective 1
Use function notation.
Slide

4. Use function notation.
When a function f is defined with a rule or an equation using x and y for the independent and dependent variables, we say, “y is a function of x” to emphasize that y depends on x. We use the notation
y = f (x),
called function notation, to express this and read f (x) as “f of x.”
y = f (x) = 9x – 5
Name of the function
Defining expression
Function value (or y-value) that corresponds to x
Name of the independent variable (or value from the domain)
Slide

5. CLASSROOM EXAMPLE 1
Evaluating a Function
Let Find the value of the function f for x = −3, which can also be written as “Find f(-3)”
Solution:
Slide

6. f (–3) f (t) Evaluating a Function Let Find the following. Solution:
CLASSROOM EXAMPLE 2
Evaluating a Function
Let Find the following.
f (–3) f (t)
Solution:
Slide

7. Let g(x) = 5x – 1. Find and simplify g(m + 2).
CLASSROOM EXAMPLE 3
Evaluating a Function
Let g(x) = 5x – 1. Find and simplify g(m + 2).
g(x) = 5x – 1
g(m + 2) = 5(m + 2) – 1
= 5m + 10 – 1
= 5m + 9
Solution:
Slide

8. f (2) = 6 f = {(2, 6), (4, 2)} f (x) = –x2 Evaluating Functions
CLASSROOM EXAMPLE 4
Evaluating Functions
Find f (2) for each function.
f = {(2, 6), (4, 2)} f (x) = –x2
f (2) = –22
f (2) = –4
Solution: x
f(x) 2 6 4
f (2) = 6
Slide

9. f (2) = 1 f (−2) = 3 f (4) = 0 Finding Function Values from a Graph
CLASSROOM EXAMPLE 5
Finding Function Values from a Graph
Refer to the graph of the function.
Find f (2).
Find f (−2).
For what value of x is f (x) = 0?
Solution:
f (2) = 1
f (−2) = 3
f (4) = 0
Slide

10. Finding an Expression for f (x)
Use function notation.
Finding an Expression for f (x)
Step 1 Solve the equation for y.
Step 2 Replace y with f (x).
Slide

11. Writing Equations Using Function Notation
CLASSROOM EXAMPLE 6
Writing Equations Using Function Notation
Rewrite the equation using function notation f (x). Then find f (1) and f (a).
x2 – 4y = 3
Step 1 Solve for y.
Solution:
Slide

12. Writing Equations Using Function Notation (cont’d)
CLASSROOM EXAMPLE 6
Writing Equations Using Function Notation (cont’d)
Find f (1) and f (a).
Step 2 Replace y with f (x).
Solution:
Slide

13. Graph linear and constant functions.
Objective 2
Graph linear and constant functions.
Slide

14. Graph linear and constant functions.
Linear Function
A function that can be defined by
f(x) = ax + b
for real numbers a and b is a linear function. The value of a is the slope m of the graph of the function. The domain of any linear function is (−∞, ∞).
Slide

15. f (x) = −1.5 Graphing Linear and Constant Functions
CLASSROOM EXAMPLE 7
Graphing Linear and Constant Functions
Graph the function. Give the domain and range.
f (x) = −1.5
Solution:
Domain: (−∞, ∞)
Range: {−1.5}
Slide

16. Practice Problems (1 of 2)
Let f(x) = 2x + 3. Find f(a+1)
Graph the following functions, provide the domain and range: a)
b) g(x) = 3
3) Let f(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find the following:
a) f(x + 2) b) f(4) – g(4)
c) f(x + h) c) f(x+h) – f(x)

17. Practice Problems (1 of 2)
4) Using the graph below, approximate values for f(-1) and f(2) 5) Rewrite the equation x2 + 4y = 6 in function notation f(x) and then find f(3)