Transformation of Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, which can include shifts, stretches, compressions, and reflections.

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CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

Front

What does a vertical shift of a function entail?

Back

A vertical shift moves the graph of the function up or down. For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down by k units.

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CCSS.HSF.BF.B.3

Front

What is a horizontal shift of a function?

Back

A horizontal shift moves the graph of the function left or right. For example, f(x - h) shifts the graph right by h units, while f(x + h) shifts it left by h units.

Tags

CCSS.HSF.BF.B.3

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

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CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

Front

What does it mean to reflect a function over the y-axis?

Back

Reflecting a function over the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. For example, f(x) becomes af(x) where a > 1.

Tags

CCSS.HSF.BF.B.3

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter. For example, f(x) becomes af(x) where 0 < a < 1.

Tags

CCSS.HSF.BF.B.3

Front

What is a horizontal stretch of a function?

Back

A horizontal stretch occurs when the input values of a function are multiplied by a factor greater than 1, making the graph wider. For example, f(x) becomes f(bx) where b < 1.

Tags

CCSS.HSF.BF.B.3

Front

What is a horizontal compression of a function?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor between 0 and 1, making the graph narrower. For example, f(x) becomes f(bx) where b > 1.

Tags

CCSS.HSF.BF.B.3

Front

How do you write the equation of a function after a vertical shift?

Back

If f(x) is the original function, after a vertical shift up by k units, the new function is f(x) + k. If shifted down by k units, it is f(x) - k.

Tags

CCSS.HSF.BF.B.3