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More Lessons for GRE Math

Math Worksheets

This lesson is part of a series of lessons for the quantitative reasoning section of the GRE revised General Test. In this lesson, we will learn:

### Graphs of Functions

The coordinate plane can be used for graphing functions. To graph a function in the *xy*-plane, we
represent each input *x* and its corresponding output *f*(*x*) as a point (*x, y*), where *y* = *f*(*x*). In other words, you use the *x*-axis for the input and the *y*-axis for the output.

The following video shows how to sketch the graph of six basic functions:*f*(*x*) = *x*, *f*(*x*) = *x*^{2}, *f*(*x*) = *x*^{3}, *f*(*x*) = square root of *x*, *f*(*x*) = cube root of *x*, *f*(*x*) = absolute value of *x*
### Piecewise Functions

### Reflection of Graphs

If the graph of *y* = *f*(*x*) is known, the

*x*-axis and the
*y*-axis

### Horizontal and Vertical Graph Transformations

In general, for any function *h*(*x*) and any positive number *c*, the following are true.

• The graph of*h*(*x*) + c is the graph of *h*(*x*) shifted upward by *c* units.

• The graph of*h*(*x*) − c is the graph of *h*(*x*) shifted downward by *c* units.

• The graph of*h*(*x* + c) is the graph of *h*(*x*) shifted to the left by *c* units.

• The graph of*h*(*x* − c) is the graph of *h*(*x*) shifted to the right by *c* units.

This video gives 9 examples to illustrate the basic outline of doing horizontal and vertical translations of graphs. This video shows some examples of horizontal and vertical translations of graphs.

###
Vertically Stretching and Shrinking Graphs

In general, for any function *h*(*x*) and any positive number *c*, the following are true.

### Graphs of Inverse Functions

###
How to find the inverse function using algebra

These videos give examples of finding the inverse of a function

More Lessons for GRE Math

Math Worksheets

This lesson is part of a series of lessons for the quantitative reasoning section of the GRE revised General Test. In this lesson, we will learn:

- how to graph some basic functions
- how to graph piece-wise defined functions
- reflection of graphs in the
*x*-axis or*y-*axis - horizontal and vertical graph transformations
- vertical stretching and shrinking graphs
- graphs of inverse functions
- how to find the inverse function using algebra

The following video shows how to sketch the graph of six basic functions:

A **piecewise-defined function** (also called a **piecewise function**) is a function whose definition changes depending on the value of the input variable.

This video shows how to evaluate and graph piece-wise functions.

This video gives 2 more examples of Graphing Piecewise Defined Functions*h*(*x*) = −*f*(*x*) is a reflection in the*x*-axis*h*(*x*) =*f*(*− x*) is a reflection in the*y*-axis

• The graph of

• The graph of

• The graph of

• The graph of

This video gives 9 examples to illustrate the basic outline of doing horizontal and vertical translations of graphs. This video shows some examples of horizontal and vertical translations of graphs.

- The graph of
*ch*(*x*) is the graph of*h*(*x*) stretched vertically by a factor of*c*if*c*> 1. - The graph of
*ch*(*x*) is the graph of*h*(*x*) shrunk vertically by a factor of*c*if 0 < c < 1.

This video shows how to graph an inverse function and points out that a graph of a function and its inverse is symmetrical about the line *y = x*.

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