Unit 1 Test Review - Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is defined as f(x) = |x|.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx - h| + k, where (h, k) is the vertex, 'a' determines the direction and steepness, and 'b' affects the width of the graph.

Front

What does the graph of an absolute value function look like?

Back

The graph of an absolute value function is a V-shape, opening upwards if 'a' is positive and downwards if 'a' is negative.

Front

What is the domain of an absolute value function?

Back

The domain of an absolute value function is all real numbers, expressed as (-∞, ∞).

Front

What is the range of an absolute value function?

Back

The range of an absolute value function is all real numbers greater than or equal to the minimum value, expressed as [k, ∞) if the vertex is at (h, k).

Front

How do you solve an absolute value equation like |x - 5| = 3?

Back

To solve |x - 5| = 3, set up two equations: x - 5 = 3 and x - 5 = -3. Solve to find x = 8 and x = 2.

Front

What does it mean if an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal a negative number, such as |x| = -3.

Front

What is the effect of the 'a' value in the function f(x) = a|x|?

Back

The 'a' value affects the vertical stretch or compression and the direction of the graph. If 'a' is positive, the graph opens upwards; if negative, it opens downwards.

Front

How do you find the vertex of an absolute value function in the form f(x) = a|bx - h| + k?

Back

The vertex is located at the point (h, k) in the coordinate plane.

Front

What is the end behavior of the graph of an absolute value function?

Back

As x approaches ±∞, the function f(x) approaches ±∞ depending on the sign of 'a'.