Can someone walk me through this?

Question

Graph the function with the given domain. Then identify the range of the function.

 

1. y=3x-2; domain: x ≥ 0

Answer 1

y = 3x - 2  ;  x ≥ 0

 

In order to graph this linear equation, you must solve for y to determine (x,y) points on the graph.

You already know that x can equal or be more than 0, and that's a great starting place.

Draw a giant T and use whole numbers to substitute for x, beginning with 0. and solve for y

 

  __X__l__Y__

      0   l   -2

      1   l    1

      2   l    4

 

1.  Let x=0.  Solve.  

     y = 3x - 2

     y= 3(0) -2

     y=  0  - 2

     y= -2

    Therefore, when x=0, y=-2

    Plot these points (0, -2) with a solid point (not open)

    The line begins here.

 

2. Let x=1. Solve.

     y = 3x - 2 

     y = 3(1) -2

     y= 3 - 2

     y= 1

     Therefore, when x= 1, y=1

     Plot these points (1, 1)

     Connect to the previous point and draw a line that continues indefinitely because x ≥ 0

 

3.  Let x=2. Solve.

 

Answer 2

A function has an  independent variable(s) [usually named x] and a dependent variable [usually named y].  There is, at most, one value of the dependent variable [y] for a given value of the independent variable(s) [x].

 

The domain describes the allowable values for the independent variables.  The range describes the allowable values of the dependent variable.

 

The equation of a line, y=3x-2, describes y as a function of x.

 

The domain (the allowable values of x) is x≥0.  That means that x is not negative; it must be either positive or else 0 (which is neither positive nor negative).

 

Now, as x takes on its allowable values (0 and larger numbers), y takes on its allowable values (-2 and larger).  [note: here is a good point for you to find the value of y when x=0].  And, as x gets larger and larger, y also gets larger and larger, only three times as fast.

 

[Notice that I have identified the range.]

 

One of the easy ways to plot line is to realize that two points determine a line.  The given equation is pretty easy for x=0 and to find y=0.  We write the coordinates as (x,y).  Plot the points:   (0,-2)  and (2/3, 0)   [after you determine how to get those values]    [you could also use the point (2,4) because it may be easier to use integers to plot]