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Example Questions
Example Question #1 : Graphing
Suppose .
To obtain the graph of , shift the graph
a distance of
units .
Upwards
To the right
Downwards
To the left
Up and right
Upwards
There are four shifts of the graph y = f(x):
y = f(x) + c shifts the graph c units upwards.
y = f(x) – c shifts the graph c units downwards.
y = f(x + c) shifts the graph c units to the left.
y = f(x – c) shifts the graph c units to the right.
Example Question #1 : Graphing
Which of the following terms are linear?
yz
x2
all of these terms are linear
x
sin(x)
x
Linear terms have only one variable in a product and no exponents other than 0 or 1. x2 has an exponent other than 0 or 1 so it is not linear. yz has two variables so is also not a linear term. Linear terms cannot have functions of variables either, so sin(x) is not linear.
We can also think of these terms somewhat like graphing equations. Linear equations are straight lines. You might recognize, for example, that x2 should be a parabola. Sin(x) has a graph that looks like a harmonic wave. Clearly these two shaps aren't straight lines!
Example Question #1 : Graphing
The slope of a line segment with points and
is:
The formula for calculating slope is rise over run, or the difference in divided by the difference in
. In this case, the difference in
is 5 while the difference in
is 5, resulting in a slope of
or 1.
Example Question #1 : Graphing
What is the slope of the linear line that passes through the origin and the point ?
Slope of a line given 2 points can be found using
.
Therefore
or
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