How does the graph of $$y = |x|$$ look?

The graph of $$y = |x|$$ is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

What is the vertex of the function $$f(x) = |x - 3| + 4$$ ?

The vertex of the function $$f(x) = |x - 3| + 4$$ is at the point (3, 4).

How do you identify the transformation from the equation $$y = -|x| + 2$$ ?

The equation $$y = -|x| + 2$$ indicates a reflection over the x-axis and a vertical shift 2 units up.

What is the general form of an absolute value function?

The general form of an absolute value function is $$f(x) = a|bx - h| + k$$ , where (h, k) is the vertex, 'a' affects the vertical stretch/compression, and 'b' affects the horizontal stretch/compression.

What does the term 'reflection' mean in the context of absolute value transformations?

Reflection in the context of absolute value transformations means flipping the graph over a specific axis, such as the x-axis or y-axis.

What is the effect of changing the sign of 'x' inside the absolute value?

Changing the sign of 'x' inside the absolute value, as in $$y = |-x|$$ , reflects the graph over the y-axis.

What is the significance of the constant term outside the absolute value?

The constant term outside the absolute value function shifts the graph vertically. For example, $$y = |x| + 3$$ shifts the graph 3 units up.

How do you determine the x-intercepts of an absolute value function?

To find the x-intercepts of an absolute value function, set the function equal to zero and solve for x.

Absolute Value Transformations Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Tags

CCSS.6.NS.C.7C

2.

FLASHCARD QUESTION

Front

What is the equation of the basic absolute value function?

Back

Tags

CCSS.HSF-IF.C.7D

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7D

4.

FLASHCARD QUESTION

Front

What effect does a negative sign have in front of the absolute value function?

Back

Tags

CCSS.HSF-IF.C.7D

5.

FLASHCARD QUESTION

Front

Back

This equation represents a transformation of the basic absolute value function, shifted 4 units to the right and 3 units up.

6.

FLASHCARD QUESTION

Front

What is the effect of multiplying the absolute value function by a factor greater than 1?

Back

7.

FLASHCARD QUESTION

Front

What is the effect of multiplying the absolute value function by a factor between 0 and 1?

Back

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