2. 2.1 (B) Functions and their Graphs

3. 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!

4. Analyzing the graph What are f(0), f(3) & f(-4)
What is the domain of f
What is the range of f
List the intercepts
How often does the line y=2 intersect the graph?
For what values of x does f(x)=-4
For what values of x is f(x) > 0

5. Analyzing the function
Consider the function:
Is the point on the graph of f?
If x = -1, what is f(x)? What point is on the graph of f?
If f(x) = 2, what is x? What point is on the graph of f?

6. Applications
Express the area of a circle as a function of its radius. State the domain of this function.

7. Manufacturing computers
The average cost C of manufacturing x computers per day is given by the function
Determine the average cost of manufacturing 30 computers a day.

8. Creating a graph of a function
Barney decides to take a walk. He leaves home, walks 2 blocks in 5 minutes at a constant speed, and realizes that he forgot to take a shower. So Barney ran home in 1 minute. While at his doorstep, it takes him 1 minute to shower up. Barney walks 5 blocks in 15 minutes and then decides to jog home. It takes him 7 minutes to get home. Draw a graph of Barney’s distance from home (in blocks) as a function of time.