Question

I am having trouble with functions on a graph. I have a line with the equation y= -1/3+ 6
How do I find the range of the function? For what value of x is f(x)=9? Could someone help me?

Answer 1

The way I think of "range" is the possible values of the y-axis on your graph. The easiest way to see this is to actually enter the function into your graphing calculator and graph it out.

In your example, you have a straight line with a slope of -1/3, so basically it's a diagonal line with values on the y-axis from (-infinity, infinity) because this diagonal line is a ray that stretch to infinity on both ends.

Here's another example. Let's say your equation now is y = 5 (horizontal line). Now your range should be {5} because that's the only possible value on your y-axis. If you get a vertical line such as x = -3, then your range will be (-infinity, infinity).

Answer 2

You wrote << I have a line with the equation
y= -1/3+ 6 >>

That just says that y = 5 2/3

Did you leave out an x somewhere?

Answer 3

Yes I did leave out the x sorry. My equation is y= -1/3x +6.

So is the range supposed to 6 or infinite?

Answer 4

infinite