Transformations of Functions

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What is a transformation of a function?

Back

A transformation of a function refers to the process of changing its position, size, or shape on a graph. This can include translations, reflections, stretches, and compressions.

Tags

CCSS.HSF.BF.B.3

Front

What does it mean for a function to be even?

Back

A function is even if it satisfies the condition f(x) = f(-x) for all x in its domain. This means the graph of the function is symmetric with respect to the y-axis.

Tags

CCSS.HSF.BF.B.3

Front

What does it mean for a function to be odd?

Back

A function is odd if it satisfies the condition f(-x) = -f(x) for all x in its domain. This means the graph of the function is symmetric with respect to the origin.

Tags

CCSS.HSF.BF.B.3

Front

What does it mean for a function to be neither even nor odd?

Back

A function is neither even nor odd if it does not satisfy the conditions for being even or odd. Its graph does not exhibit symmetry with respect to the y-axis or the origin.

Tags

CCSS.HSF.BF.B.3

Front

How do you determine if a function is even?

Back

To determine if a function is even, replace x with -x in the function's equation. If the resulting expression is identical to the original function, it is even.

Tags

CCSS.HSF.BF.B.3

Front

How do you determine if a function is odd?

Back

To determine if a function is odd, replace x with -x in the function's equation. If the resulting expression is the negative of the original function, it is odd.

Tags

CCSS.HSF.BF.B.3

Front

What is a vertical translation of a function?

Back

A vertical translation of a function involves shifting the graph up or down without changing its shape. This is done by adding or subtracting a constant from the function.

Front

What is a horizontal translation of a function?

Back

A horizontal translation of a function involves shifting the graph left or right. This is achieved by adding or subtracting a constant from the variable x in the function.

Front

What is a reflection of a function across the x-axis?

Back

A reflection across the x-axis occurs when the output values of the function are multiplied by -1. This flips the graph over the x-axis.

Tags

CCSS.HSF.BF.B.3

Front

What is a reflection of a function across the y-axis?

Back

A reflection across the y-axis occurs when the input values of the function are replaced with their negatives. This flips the graph over the y-axis.

Tags

CCSS.HSF.BF.B.3