What is the graph of the function $$y = |x|$$ ?

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

How does the graph of $$y = |x| + 2$$ differ from $$y = |x|$$ ?

The graph of $$y = |x| + 2$$ is the same as $$y = |x|$$ but shifted upwards by 2 units.

What effect does the negative sign have in $$y = -|x|$$ ?

The negative sign in $$y = -|x|$$ reflects the graph of $$y = |x|$$ across the x-axis, resulting in an upside-down V shape.

What does the coefficient in front of $$|x|$$ indicate in $$y = a|x|$$ ?

The coefficient 'a' in $$y = a|x|$$ affects the steepness of the graph. If |a| > 1, the graph is steeper; if 0

What is the vertex of the function $$y = |x - 2|$$ ?

The vertex of the function $$y = |x - 2|$$ is at the point (2, 0). This is where the graph changes direction.

How do you find the x-intercepts of the function $$y = |x + 3| - 1$$ ?

To find the x-intercepts, set $$|x + 3| - 1 = 0$$ . This gives $$|x + 3| = 1$$ , leading to two equations: $$x + 3 = 1$$ and $$x + 3 = -1$$ .

What is the effect of adding a constant to an absolute value function, such as in $$y = |x| + c$$ ?

Adding a constant 'c' to an absolute value function shifts the graph vertically. If c > 0, it shifts up; if c

What is the domain of the function $$y = |x|$$ ?

The domain of the function $$y = |x|$$ is all real numbers, expressed as @@(- ext{∞}, ext{∞})@@.

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

The range of the function $$y = |x|$$ is all non-negative real numbers, expressed as $$[0, \text{∞})$$ .

How does the graph of $$y = |x - 1| - 3$$ look compared to $$y = |x|$$ ?

The graph of $$y = |x - 1| - 3$$ is the graph of $$y = |x|$$ shifted right by 1 unit and down by 3 units.

What is the significance of the point where the graph of an absolute value function touches the x-axis?

The point where the graph touches the x-axis represents the x-intercept, which is the solution to the equation $$|x| = 0$$ .

What is the equation of the line of symmetry for the graph of $$y = |x - 4|$$ ?

The line of symmetry for the graph of $$y = |x - 4|$$ is the vertical line $$x = 4$$ .

What happens to the graph of $$y = |x|$$ when you replace x with -x?

Replacing x with -x in $$y = |x|$$ does not change the graph, as absolute value functions are even functions and symmetric about the y-axis.

How do you determine the transformations applied to the graph of $$y = |x|$$ to get to $$y = 2|x + 1| - 3$$ ?

The graph of $$y = |x|$$ is shifted left by 1 unit, vertically stretched by a factor of 2, and then shifted down by 3 units.

Graphing Absolute Value Functions Flashcards

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FLASHCARD QUESTION

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What is an absolute value function?

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CCSS.HSF-IF.C.7D

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CCSS.HSF-IF.C.7D

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CCSS.HSF-IF.C.7D

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