Lessons with videos, examples and solutions to help PreCalculus students learn how about parent functions and their graphs.

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More Graphs And PreCalculus Lessons

Graphs Of Functions

The following figures show the graphs of parent functions: linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent. Scroll down the page for more examples and solutions.

The following table shows the transformation rules for functions. Scroll down the page for examples and solutions on how to use the transformation rules.

In math, we often encounter certain elementary functions. These elementary functions include rational functions, exponential functions, basic polynomials, absolute values and the square root function. It is important to recognize the graphs of elementary functions, and to be able to graph them ourselves. This will be especially useful when doing transformations.

Basic graphs that are useful to know for any math student taking algebra or higher.

y = mx + b (linear function)

y = x^{2} (quadratic)

y = x^{3} (cubic)

y = x^{5}

y = |x| (absolute)

y = √x (square root)

y = 1/x (reciprocal)

y = 1/x^{2}

y = log_{b}(x) for b > 1

y = a^{x} for a > 1 (exponential)

y = a^{x} for 0 < a < 1

f(x) = x

f(x) = x^{2}

f(x) = x^{3}

f(x) = √x

f(x) = cube root(x)

f(x) = |x|

y = x

y = x^{2}

y = √x

y = x^{3}

y = 1/x

y = 1/x^{2}

y = |x|

In math, every function can be classified as a member of a family. Each member of a family of functions is related to its simpler, or most basic, function sharing the same characteristics. This function is called the parent function.

This lesson discusses some of the basic characteristics of linear, quadratic, square root, absolute value and reciprocal functions.

Learn how to shift graphs up, down, left, and right by looking at their equations.

Vertical Shifts:

f(x) + c moves up,

f(x) - c moves down.

Horizontal Shifts:

f(x + c) moves left,

f(x - c) moves right.

Looking at some parent functions and using the idea of translating functions to draw graphs and write equations.

y = x,

y = x^{2},

y = x^{3},

y = √x,

y = 1/x,

y = |x|,

x^{2} + y^{2} = 9 (circle),

y = b^{x}

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