College Algebra
Tutorial 31: Graphs of Functions, Part I:
Graping Functions by Plotting Points
Learning Objectives
Introduction
Tutorial
On a graph, the domain corresponds to the horizontal axis. Since that is the case, we need to look to the left and right to see if there are any end points to help us find our domain. If the graph keeps going on and on to the right then the domain is infinity on the right side of the interval. If the graph keeps going on and on to the left then the domain is negative infinity on the left side of the interval.
On a graph, the range corresponds to the vertical axis. Since that is the case, we need to look up and down to see if there are any end points to help us find our range. If the graph keeps going up with no endpoint then the range is infinity on the right side of the interval. If the graph keeps going down then the range goes to negative infinity on the left side of the interval.
Keep in mind that these are the basic shapes of these graphs. They can be shifted and stretched depending on the function given. A major goal is to recognize what type of function you are graphing and predict the basic shape from that before you even start.
Note that the domain and ranges that go with each one are also given.
Linear Function
Domain:
Range:
Domain:
Range:
Domain:
Range:
Domain:
Range:
Domain:
Range:
Domain:
Range:
x = -3, -2, -1, 0, 1, 2, 3
We will use the seven values of x that were given to find corresponding functional values to give us seven ordered pair solutions.
Keep in mind that the functional value that we find correlates to the second or y value of our ordered pair.
Since that is the case, we need to
look to the
left and right and see if there are any end points. In
this case, note how the curve has
arrows at both
ends, that means it would go on and on forever to the right and to the
left.
This means that the domain is .
Since that is the case, we need to look up and down and see if there are any end points. In this case, note how the curve has a low endpoint of y = -5 and it has arrows at both ends going up, that means it would go up on and on forever.
This means that the range is.
x = 0, 1, 4, 9
We will use the four values of x that were given to find corresponding functional values to give us four ordered pair solutions.
Keep in mind that the functional value that we find correlates to the second or y value of our ordered pair.
Since that is the case, we need to
look to the
left and right and see if there are any end points. In
this case, note how there is a left
endpoint
at x = 0. Also note that the curve
has
an arrow going to the right, that means it would go on and on
forever
to the right.
This means that the domain is .
Since that is the case, we need to
look up and
down and see if there are any end points. In this case,
note
how the curve has a low endpoint of y =
3 and
it has an arrow going up, that means it would go on and on
forever
up.
This means that the range is.
x = 0, 1, 2, 3, 4, 5, 6
We will use the seven values of x that were given to find corresponding functional values to give us seven ordered pair solutions.
Keep in mind that the functional value that we find correlates to the second or y value of our ordered pair.
Since that is the case, we need to
look to the
left and right and see if there are any end points. In
this case, note how there are arrows
at both
ends, that means it would go on and on forever to the right and to the
left.
This means that the domain is .
Since that is the case, we need to look up and down and see if there are any end points. In this case, note how the graph has a low endpoint of y = 0 and it has an arrows that go up, that means it would go up on and on forever.
This means that the range is.
x = -3, -2, -1, 0, 1, 2, 3
We will use the seven values of x that were given to find corresponding functional values to give us seven ordered pair solutions.
Keep in mind that the functional value that we find correlates to the second or y value of our ordered pair.
Since that is the case, we need to
look to the
left and right and see if there are any end points. In
this case, note how the curve has
arrows at both
ends, that means it would go on and on forever to the right and to the
left.
This means that the domain is .
Since that is the case, we need to look up and down and see if there are any end points. In this case, note how the line does not go up or down and that all the values of y are -2.
This means that the range is {y | y = -2}.
x = -2, -1, 0, 1, 2
We will use the five values of x that were given to find corresponding functional values to give us five ordered pair solutions.
Keep in mind that the functional value that we find correlates to the second or y value of our ordered pair.
Since that is the case, we need to
look to the
left and right and see if there are any end points. In
this case, note how the curve has
arrows at both
ends, that means it would go on and on forever to the right and to the
left.
This means that the domain is .
Since that is the case, we need to look up and down and see if there are any end points. In this case, note how the curve has arrows at both ends, that means it would go on and on forever up and down.
This means that the range is.
Practice Problems
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1e: Graph the given function using the given values of x. Also use the graph to determine the domain and range of the function.
Need Extra Help on these Topics?
The following are webpages
that can assist
you in the topics that were covered on this page:
Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.
Last revised on April 7, 2010 by Kim Seward.
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