2.1 (B) Functions and their Graphs

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Presentation transcript:

2.1 (B) Functions and their Graphs

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!

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

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?

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

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.

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.