1. Dr. Fowler  AFM  Unit 1-2
The Graph of a Function

2. EXAMPLE – Identifying the Graph of a Function:
Theorem – Vertical line TEST… A set of points in the xy-plane is the graph of a function if and only if every vertical line intersects the graph in at most one point.
EXAMPLE – Identifying the Graph of a Function:
Which of the following are graphs of functions?
A Function
A Function

3. EXAMPLE – Identifying the Graph of a Function:
Which of the following are graphs of functions?
Not A Function
Not A Function

4. ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3 Evaluating Functions:
Output value
Input value
Output value
Input value
ƒ(x) = 5x + 3
ƒ(1) = 5(1) + 3
ƒ of x equals 5 times x plus 3.
ƒ of 1 equals 5 times 1 plus 3.
f(x) is not “f times x” or “f multiplied by x.” f(x) means “the value of f at x.” So f(1) represents the value of f at x =1
Caution

5. The function described by ƒ(x) = 5x + 3 is the same as the function described by y = 5x + 3. And both of these functions are the same as the set of ordered pairs (x, 5x+ 3).
y = 5x (x, y) (x, 5x + 3)
Notice that y = ƒ(x) for each x.
ƒ(x) = 5x (x, ƒ(x)) (x, 5x + 3)
The graph of a function is a picture of the function’s ordered pairs.

6. Video - Evaluating Functions: https://www. youtube. com/watch
Pay close attention.
Take Notes.

7. Example 1A: Evaluating Functions
For each function, evaluate ƒ(0), ƒ , and ƒ(–2).
ƒ(x) = 8 + 4x
Substitute each value for x and evaluate.
ƒ(0) = 8 + 4(0) = 8
ƒ = = 10
ƒ(–2) = 8 + 4(–2) = 0

8. Example 1B: Evaluating Functions
For each function, evaluate ƒ(0), ƒ , and ƒ(–2).
Use the graph to find the corresponding y-value for each x-value.
ƒ(0) = 3
ƒ = 0
ƒ(–2) = 4

9. For each function, evaluate ƒ(0), ƒ , and ƒ(–2).
Example – LET US ALL TRY THIS BY OURSELVES:
For each function, evaluate ƒ(0), ƒ , and ƒ(–2).
ƒ(x) = –2x + 1

10. Example
Graph the function.
Graph the points.
Do not connect the points because the values between the given points have not been defined.

11. NOTES: In the notation ƒ(x), ƒ is the name of the function
NOTES: In the notation ƒ(x), ƒ is the name of the function. The output ƒ(x) of a function is called the dependent variable because it depends on the input value of the function. The input x is called the independent variable. When a function is graphed, the independent variable is graphed on the horizontal axis and the dependent variable is graphed on the vertical axis.

12. Find X Min-Max
Find Y Min-Max
Four times.

13. Yes

14. What are the x- and y-intercepts?
The x-intercept is where the graph crosses the x-axis. The y-coordinate is always 0 for the x-intercept. The y-intercept is where the graph crosses the y-axis. The x-coordinate is always 0 for the y-intercept.
(2, 0)
(0, 6)

15. Find the x- and y-intercepts. 1. x - 2y = 12
x-intercept: Plug in 0 for y.
x - 2(0) = 12
x = 12; (12, 0)
y-intercept: Plug in 0 for x.
0 - 2y = 12
y = -6; (0, -6)

16. Excellent Job !!! Well Done