How does the graph of $$f(x) = |x|$$ transform when we apply a vertical shift?

A vertical shift moves the graph up or down. For example, $$f(x) = |x| + 2$$ shifts the graph up by 2 units.

What happens to the graph of an absolute value function when you subtract a constant from it?

Subtracting a constant shifts the graph down. For example, $$f(x) = |x| - 3$$ shifts the graph down by 3 units.

What is the transformation represented by the function $$f(x) = |x + 4| - 5$$ ?

This function represents a left shift by 4 units and a downward shift by 5 units.

How do you determine the vertex of an absolute value function?

The vertex of an absolute value function $$f(x) = a|x - h| + k$$ is the point (h, k).

What is the significance of the vertex in the graph of an absolute value function?

The vertex is the point where the graph changes direction and is the minimum or maximum point of the function.

What does the term 'opening direction' refer to in absolute value functions?

The opening direction refers to whether the graph opens upwards (positive a) or downwards (negative a).

How can you identify the transformations applied to the parent function from the equation of an absolute value function?

You can identify transformations by examining the values of h and k in the function $$f(x) = a|x - h| + k$$ .

What is the general form of an absolute value function?

The general form of an absolute value function is $$f(x) = a|x - h| + k$$ , where (h, k) is the vertex.

How do you graph an absolute value function?

To graph an absolute value function, identify the vertex, plot points on either side of the vertex, and connect them to form a V shape.

Absolute Value Functions Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of an absolute value function?

Back

2.

FLASHCARD QUESTION

Front

What is the parent function of absolute value?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What effect does a horizontal shift have on the graph of an absolute value function?

Back

5.

FLASHCARD QUESTION

Front

What does a negative sign in front of an absolute value function indicate?

Back

6.

FLASHCARD QUESTION

Front

How do you represent the absolute value of a number mathematically?

Back

7.

FLASHCARD QUESTION

Front

What is the effect of multiplying an absolute value function by a positive constant?

Back

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