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Question 1196402: find the domain and range of function f(x)=3x-2 and sketch a graph for this
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! Line. Domain All Real Numbers.
You know how to graph f because you can read x-axis intercept and slope directly from the function.
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Domain = All real numbers
Range = All real numbers
As an inequality we can say
Domain is 
Range is 
The interval notation for each is ) to represent going from negative infinity to positive infinity. Use curved parenthesis for both types of infinity. This is because we cannot reach these endpoints.
The domain represents the set of possible inputs.
The range represents the set of possible outputs.
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To graph this, we need two points to draw a straight line
Compare the equation y = 3x-2 to the form y = mx+b
m = 3 = 3/1 = slope
b = -2 = y intercept
The y intercept b = -2 tells us that (0,-2) is one point on the line
Then move up 3 and to the right 1 (based on what the slope says) to arrive at the point (1,1)
Therefore, you can draw a straight line through (0,-2) and (1,1) to graph out y = 3x-2
You don't have to start at the anchor point of (0,-2) as you can start anywhere you like. But you have to be on the line.
Another way to graph:
Plug in x = 0 to find that...
y = 3x-2
y = 3(0)-2
y = 0-2
y = -2
Therefore, the ordered pair (x,y) = (0,-2) is on the line
Repeat for x = 1
y = 3x-2
y = 3(1)-2
y = 3-2
y = 1
So (x,y) = (1,1) is another ordered pair point.
We get (0,-2) and (1,1) like we found earlier.
There's nothing particularly special about x = 0 and x = 1. You can pick any two x values you want. After all the domain is the set of all real numbers.
I went with those values because they're small and easy to work with. Also, most standard xy grids are centered around the origin.
Feel free to choose your favorite two numbers to use for x.
You can use graphing software to verify your work. I recommend it to check your work rather than do it entirely for you.
Desmos and GeoGebra are two free options, among many others.
Here's the link to the Desmos graph so you can interact with it.
https://www.desmos.com/calculator/bawhrkdr7a
Take note how the graph stretches forever left and right. This visually confirms why the domain is the set of all real numbers.
Any number can replace x. Hence we have infinitely many (x,y) points to work with.
All points on this line are of the form (x, 3x-2) meaning that the y coordinate depends on what you picked for x.
Similarly, the graph stretches up and down forever. This means any output (y) is possible and it visually confirms why the range is the set of all real numbers.
The domain and range being "all real numbers" applies to any diagonal linear equation (i.e. when the slope is nonzero, and is defined).
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