# GRE Math : Graphing

## Example Questions

### Example Question #1 : How To Graph A Function

Suppose

To obtain the graph of , shift the graph  a distance of  units              .

To the right

Upwards

To the left

Up and right

Downwards

Upwards

Explanation:

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 #291 : Geometry

Which of the following terms are linear?

yz

x

all of these terms are linear

sin(x)

x2

x

Explanation:

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 #291 : Geometry

The slope of a line segment with points  and  is:

Explanation:

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 ?

Explanation:

Slope of a line given 2 points can be found using

.

Therefore

or

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