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High School Algebra II: Help and Review26 chapters | 296 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, learn how you can differentiate from the eight most common types of functions and their graphs. Learn the distinct look of each so you can easily distinguish them from each other.

There are eight types of graphs that you will see more often than other types. Each has its own type of function that produces the graphs. They are easy to visually distinguish and by knowing how each looks, you can get an idea of what a graph might look like just by analyzing the function. The eight types are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.

**Linear** graphs are produced by linear functions of this form:

Linear functions have variables to the first degree and have two constants that determine the location of the graph. These functions always graph into a line. The constant *m* determines whether the line slopes down or up. If it is positive, the line will slope up, and if it is negative, then the line will slope down.

**Power** graphs are produced by functions with only one term and a power. The power can be positive, negative, or even a fraction.

The graphs that these types of functions produce vary depending on the power. If the power is positive, the graph changes direction based on the number of the power. If the power is even, the graph will have both edges going in the same direction. If the power is odd, the graph will have one edge going up and another going down. If the power is negative, it will have two parts. Each part will avoid the x=0 line because that will cause division by zero. When the power is a fraction, the graph goes up at x=0 and then when *y* is positive, it starts curving towards the x-axis.

**Quadratics** are functions where the highest power is two.

They graph into parabolas. The constants *a*, *b,* and *c* determine the location of the parabola on the graph. The *a* tells you whether the parabola will open up or down. If it's positive, it will open up and smile. If it's negative, it will open down and frown.

**Polynomials** are a more general function than a quadratic and allow for higher powers that are still whole numbers.

These functions produce more interesting graphs with more curves. The highest power of the function tells you how many curves or ups and downs the graph may have.

**Rational** graphs are from functions that are the division of two polynomials. When these are graphed, you will see the graph split into parts. The areas that the graph avoids are where division by zero happens.

**Exponentials** are where the *x* variable is the power.

When *b* is greater than one, then you will see exponential growth occur. If it is less than one but greater than zero, you will see exponential decay. Growth is when the graph rises to the right. Decay is when it drops to the right.

**Logarithmic** functions involve the graphing of logarithms.

These graphs are similar to the exponentials except they rise earlier and grow slower.

**Sinusoidal** graphs use functions that have the sine function inside.

The graph shows up as a wave pattern.

Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each has a unique graph that is easy to visually differentiate from the rest.

You might see other types of graphs that aren't listed here. That's because there are many different types of functions, and the more you continue learning math, the more you will get exposed to. What you have learned in this lesson is a good beginning framework for the types of graphs you will see.

After you have finished this lesson, you should be able to name and identify the eight most commonly used graphs.

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High School Algebra II: Help and Review26 chapters | 296 lessons

- Graphing Basic Functions 8:01
- Compounding Functions and Graphing Functions of Functions 7:47
- Understanding and Graphing the Inverse Function 7:31
- Polynomials Functions: Properties and Factoring 7:45
- Polynomials Functions: Exponentials and Simplifying 7:45
- Exponentials, Logarithms & the Natural Log 8:36
- Slopes and Tangents on a Graph 10:05
- Equation of a Line Using Point-Slope Formula 9:27
- Horizontal and Vertical Asymptotes 7:47
- Implicit Functions 4:30
- Graphs: Types, Examples & Functions 5:06
- Finding Absolute Extrema: Practice Problems & Overview
- Vertical Asymptotes: Definition & Rules 4:29
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