Answers: Part 1 (the ovals) Domain = {-6,-1,1,5,7} Range = {-4,-1,2,4} ------------------- Part 2 (the table) Domain = {1,-3,-2} Range = {-2,5,1} ------------------- Part 3 (the graph) Domain = {1, 2, 3, 4, 5, 6} Range = {-1, 0, 1, 2, 3, 6}
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Explanation:
Part 1 (the ovals) The domain is the set of input values of a function. The input oval is the one on the left. All we do is list the numbers in the input oval to get this list: {-6,-1,1,5,7} The curly braces tell the reader that we're talking about a set of values. So this is the domain.
The range is the same way but with the output oval on the right side List those values in the right oval and we have {-4,-1,2,4} Which is the range. That's all there is to it.
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Part 2 (The tables)
Like with the ovals in part 1, we simply list the input values. The x values are the input values. Notice how this list is on the left side to indicate inputs. So that's why the domain is {1, -3, -2}. Optionally you can sort from smallest to largest if you want. Doing so leads to {-3, -2, 1}
The range is {-2,5,1} for similar reasons. Simply look at the y column
Side Note: we haven't had to do it so far, but if we get duplicate values then we must toss them. ------------------------------ Part 3 (the graph)
Using a pencil, draw vertical lines that lead from each point to the x axis. You'll notice that you touch the x axis at the following numbers: 1, 2, 3, 4, 5, 6 So the domain is the list of those x values (similar to part 2) and it is {1, 2, 3, 4, 5, 6}
Erase your pencil marks from earlier. Draw horizontal lines from each point to the y axis. The horizontal lines will arrive at these y values: -1, 0, 1, 2, 3, 6 So that's why the range is {-1, 0, 1, 2, 3, 6}
First you'll find the equation of the graphed line in slope-intercept form, y = mx+b, and then from there we'll convert it into standard form, ax+by = c.
To find the slope of the line you could either use the two points on the line or just look and see.
Start from the point farther down, the point on (5,0). Look and see how many units it takes to go up/down to where the point on (0,3) is.
If it goes up, then you are at a positive slope so far. If it goes down, then you are at a negative slope so far. It takes 3 units UP (positive) to go onto the line that (0,3) is on.
Now see how far does it take to go left/right to where the point on (0,3) is. If you have to go left, that means you have a negative; if it goes right then you have a positive. It takes 5 units LEFT (negative) to where (0,3) is.
A positive (up) and a negative (left) make a negative, so your slope is how many units it took to go vertically/how many units it took to go horizontally.
Your slope is -3/5.
Now to solve for b, or the y-intercept, you can look on the graph to see where the point lies on the y-axis (vertical). The point lies on 3 on the y-axis, so your y-intercept is 3.
Since you have the slope and can see the y-intercept of the graphed line, you can make the equation y = mx+b by plugging in -3/5 for the slope and plugging in 3 for b (y-intercept).
y = (-3/5)x+(3)
Remove the parentheses: y = -3/5x+3.
Now to convert from slope-intercept form into standard form, you will have to move everything to the left side and leave only b, or 3.
Add -3/5x to both sides.
3/5x+y = 3
You can't have a fraction in standard form, so multiply everything in the equation by 5.
