How do you solve an equation involving absolute value, such as $$|x| = a$$ ?

To solve $$|x| = a$$ , you set up two equations: $$x = a$$ and $$x = -a$$ .

What is the range of the function $$y = |x| + 2$$ ?

The range of the function $$y = |x| + 2$$ is $$y \ge 2$$ .

What is the solution to the equation $$|2a - 10| = 6$$ ?

The solutions are $$a = 8$$ and $$a = 2$$ .

What is the absolute value of $$-5$$ ?

The absolute value of $$-5$$ is $$5$$ .

What is the solution to the equation $$|-2n| + 10 = -50$$ ?

There is no solution to the equation $$|-2n| + 10 = -50$$ .

What is the domain of the function $$f(x) = |x|$$ ?

The domain of the function $$f(x) = |x|$$ is all real numbers, or $$(-\infty, \infty)$$ .

How do you graph a piecewise function?

To graph a piecewise function, plot each piece according to its defined interval and connect them appropriately.

What is the value of $$g(7)$$ if $$g(x) = 2x + 3$$ ?

The value of $$g(7)$$ is $$17$$ .

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

Adding a constant $$c$$ to an absolute value function shifts the graph vertically by $$c$$ units.

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

The vertex of an absolute value function is the point where the graph changes direction, typically at the minimum or maximum value.

How do you determine if a piecewise function is continuous?

A piecewise function is continuous if the limits from both sides of a point match the function's value at that point.

Piecewise Functions & Absolute Value Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

2.

FLASHCARD QUESTION

Front

What does the absolute value of a number represent?

Back

The absolute value of a number represents its distance from zero on the number line, regardless of direction.

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