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

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

What does the equation $$y = |x - h|$$ represent?

The equation $$y = |x - h|$$ represents a horizontal shift of the parent function $$y = |x|$$ to the right by h units if h > 0, and to the left by h units if h

What does the equation $$y = -|x|$$ represent?

The equation $$y = -|x|$$ reflects the graph of the parent function $$y = |x|$$ across the x-axis.

How do you determine the vertex of the absolute value function $$y = |x - h| + k$$ ?

The vertex of the function $$y = |x - h| + k$$ is at the point (h, k).

What is the domain of the absolute value function?

The domain of the absolute value function is all real numbers, expressed as @@(- ext{∞}, ext{∞})@@.

What is the range of the absolute value function $$y = |x|$$ ?

The range of the absolute value function $$y = |x|$$ is all real numbers greater than or equal to 0, expressed as $$[0, \text{∞})$$ .

How do you find the x-intercepts of the absolute value function $$y = |x - 3|$$ ?

To find the x-intercepts of $$y = |x - 3|$$ , set y to 0 and solve for x: $$|x - 3| = 0$$ , which gives x = 3.

What does the equation $$y = |x + 2| - 4$$ represent in terms of transformations?

The equation $$y = |x + 2| - 4$$ represents a left shift of 2 units and a downward shift of 4 units from the parent function $$y = |x|$$ .

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

The vertex of an absolute value graph is the point where the graph changes direction; it represents the minimum or maximum value of the function.

How do you graph the equation $$y = -|x + 1| + 2$$ ?

To graph $$y = -|x + 1| + 2$$ , start with the vertex at (-1, 2), reflect the V-shape downwards, and plot points to show the graph opening downwards.

What is the effect of a negative coefficient in front of the absolute value function?

A negative coefficient in front of the absolute value function, such as in $$y = -|x|$$ , reflects the graph across the x-axis.

Graphing Absolute Value Equations Flashcards

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FLASHCARD QUESTION

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What is the definition of an absolute value function?

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