GRE Math : Graphing
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Example Questions
Example Question #1 : How To Graph A Function
Suppose 
To obtain the graph of 
Upwards
To the left
To the right
Downwards
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 #102 : Coordinate Geometry
Which of the following terms are linear?
yz
sin(x)
all of these terms are linear
x
x2
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 
The formula for calculating slope is rise over run, or the difference in 
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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