How to find function of these ordered pairs?

Question

Hi, I need help with solving : 

 

Let f = (-4,2) (2,2) (3,-4) (0,-3) (-3,1) ( -2,-2) ( 1,0). Find f(0) , f(-4), f(f(-3) and evaluate x where f(x) =1 

 

 

I don't have a solid understanding of functions as I am just beggining it so can you please show me steps please.

Answer 1

The independent variable is usually called x; the dependent variable is called y.

 

A function has, at most, one y-value [called f(x)] for each x-value.The function does not need to be a "smooth" curve when plotted (that is, it does not have to be defined for points not originally listed), but the "vertical line test" reveals whether there are two possible y-values for a single x-value.

 

Each x-value is input to f(x) and it produces a y-value as output.  This is how the list of points were created.

 

What is f(0)?   It is the y-value from the point (0,y).  That point is (0,-3), so f(0)=-3.

 

What is f(-4)?  It is the y-value from the point (-4.y).  That point it (-4,2), so f(-4)=2.

 

Now, f(f(x)) uses the y-values from the function as input and finds the function again.  That means that we find points (y,z) such that z=f(y) using the same function.

 

What is f(f(-3))?  Well, f(-3)=1  [see points].  Now, what is f(1)?  f(1)=0  [again, see points].  So, f(f(-3))=0.

 

Finally, what is x when f(x)=1?   Once more, look at the points.  the x-value is -3 when the y-value is 1 at point (-3,1)  [see points].  Therefore, f(-3)=1.

 

Now, just to check whether you are getting this:

     What is f(-2)?

     What is f(f(-2))?

     What is f(f(f(f(f(-2)))))?