Functions, Graphs and Features

Below is an example of a relation that is a function and an example of a relation that is not a function. 

What are the defining characteristics of a function? 

FUNCTION:

NOT A FUNCTION:

Use the graph below to answer the questions that follow: 

Function notation describes a particular relationship and implies the dependency of variables. 

The general form of function notation is $${f(x) = y}$$.  $$y$$ is dependent on $${x }$$.

Part A: 
The function $$f$$ above has a point $$f(-2) = 1$$. Mark this point on the graph above. 

Part B: 
Find the $$x$$ or $$y$$ values from the graph noted by the function notation below. 

$$f(-9)=$$

$$f(x)=1$$

$$f(x)=-2$$

$$f(4)=$$

$$g(x)=5$$

$${g(0)=}$$

John was running a race, and his coach was timing him. John’s race can be described as the distance in meters, $$d$$, as a function of time in seconds, $$t$$.  Partway through the race, John’s position could be described as $$d(6)=50$$. Describe John’s time and distance at this point. 

Suppose $$f$$ is a function. 

1. If $$10 = f(-4)$$, give the coordinates of a point on the graph of $$f$$. 
2. If 6 is a solution to the equation $$f(w) = 1$$, give a point on the graph of $$f$$. 

Let $${f(t)}$$ be the number of people, in millions, who own cell phones $$t$$ years after 1990. Explain the meaning of the following statements. 

1. $${f(10)=100.3}$$
2. $${f(a)=20}$$
3. $${f(20)=b}$$ 
4. $$n= {f(t)}$$