Examples, solutions, videos, and lessons to help High School students
learn how to identify the effect on the graph of replacing *f*(*x*)
by *f*(*x*) + *k*,* k**f*(*x*),
*f*(*kx*), and *f*(*x* + *k*) for
specific values of *k* (both positive and negative); find the value
of *k* given the graphs. Experiment with cases and illustrate an explanation
of the effects on the graph using technology. Include recognizing even and odd functions from
their graphs and algebraic expressions for them.

Common Core (Functions)

Common Core Mathematics

Common Core: HSF-BF.B.3

The following table gives the transformation rules for functions: Vertical and horizontal translations, Reflection over the x-axis and y-axis, Vertical and horizontal stretch, Vertical and horizontal compression. Scroll down the page for examples and solutions on how to use the transformation rules.This video explains to graph graph horizontal and vertical stretches and compressions in the form a*f(b(x-c))+d. This video looks at how a and b affect the graph of f(x).

af(x): a > 1, stretch f(x) vertically by a factor of a

af(x): 0 < a < 1, compress f(x) vertically by a factor of a

f(bx); b > 1, compress f(x) horizontally

f(bx); 0 < b < 1, stretch f(x) horizontally.

This video explains to graph graph horizontal and vertical translation in the form a*f(b(x-c))+d. This video looks at how c and d affect the graph of f(x).

f(x + c): shift f(x) c units left

f(x − c): shift f(x) c units right

f(x) + d: shift f(x) d units up

f(x) − d: shift f(x) d units down

This video reviews function transformation including stretches, compressions, shifts left, shifts right, and reflections across the x and y axes.

This video explains how to identify a shift up, down, left, and right given the translation in function notation.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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