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

Reflecting a function across the x-axis means flipping the graph over the x-axis. This is represented by multiplying the function by -1, e.g., $$f(x) = -x$$ .

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

Reflecting a function across the y-axis means flipping the graph over the y-axis. This is represented by replacing $$x$$ with $$-x$$ in the function, e.g., $$f(x) = f(-x)$$ .

How do you identify the equation of a transformed linear function?

To identify the equation of a transformed linear function, observe the transformations applied to the parent function $$f(x) = x$$ . For example, if the function is translated up by 3 and stretched vertically by a factor of 2, the equation would be $$f(x) = 2x + 3$$ .

What is the parent function for linear transformations?

The parent function for linear transformations is $$f(x) = x$$ . It is the simplest form of a linear function and serves as the basis for all transformations.

What is the effect of a negative coefficient on a linear function?

A negative coefficient in front of a linear function reflects the graph across the x-axis. For example, $$f(x) = -x$$ is a reflection of the parent function $$f(x) = x$$ .

What does it mean for a function to be stretched horizontally?

Horizontal stretching occurs when the graph of a function is stretched away from the y-axis. This is represented by replacing $$x$$ with $$kx$$ where $$0

What does it mean for a function to be compressed horizontally?

Horizontal compression occurs when the graph of a function is compressed towards the y-axis. This is represented by replacing $$x$$ with $$kx$$ where $$k > 1$$ .

How can you determine the transformations applied to a function from its equation?

To determine the transformations applied to a function from its equation, compare it to the parent function $$f(x) = x$$ and identify changes in coefficients and constants that indicate translations, stretches, or reflections.

Lesson 3-5 Transformations of Linear Functions Flashcards

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FLASHCARD QUESTION

Front

What is a transformation of a function?

Back

A transformation of a function refers to a change in the position, size, or shape of its graph. Common transformations include translations, reflections, stretches, and compressions.

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