Answer :
When the domain is ≥ to 0, that basically means that x must be ≥ 0.
Imagine what that looks like.
It would just be the right side of the coordinate plane, right? Because the left side would have negative x values.
We're basically just going to be graphing the line [tex]y=3x-2[/tex], except only the part on the right side of the coordinate plane because of course x ≥ 0.
When you have an equation in the form of [tex]y=mx+b[/tex], [tex]b[/tex] is going to be the y-intercept (the point where the line intersects the y-axis) and [tex]m[/tex] is going to be the slope.
Since the y-intercept is -2, draw a point at (0, -2).
Then, use the slope to find another point on the line.
The slope is 3, which as a fraction would be [tex]\frac{3}1[/tex].
Slope = rise over run, so basically every change of 1 in x = a change of 3 in y.
Draw a point 3 up and 1 over from (0, -2). (at (1, 1))
Then draw a line through the two points we have graphed. Don't draw past the y-axis on the left side, because of course x ≥ 0.
And there you go!
The range of the function is basically the possible values y can have.
Well, since it's not going any lower than the y-intercept (0, -2), the range is ≥ -2.
Imagine what that looks like.
It would just be the right side of the coordinate plane, right? Because the left side would have negative x values.
We're basically just going to be graphing the line [tex]y=3x-2[/tex], except only the part on the right side of the coordinate plane because of course x ≥ 0.
When you have an equation in the form of [tex]y=mx+b[/tex], [tex]b[/tex] is going to be the y-intercept (the point where the line intersects the y-axis) and [tex]m[/tex] is going to be the slope.
Since the y-intercept is -2, draw a point at (0, -2).
Then, use the slope to find another point on the line.
The slope is 3, which as a fraction would be [tex]\frac{3}1[/tex].
Slope = rise over run, so basically every change of 1 in x = a change of 3 in y.
Draw a point 3 up and 1 over from (0, -2). (at (1, 1))
Then draw a line through the two points we have graphed. Don't draw past the y-axis on the left side, because of course x ≥ 0.
And there you go!
The range of the function is basically the possible values y can have.
Well, since it's not going any lower than the y-intercept (0, -2), the range is ≥ -2.
