Graphing Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, always resulting in a non-negative output.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx + c| + d, where 'a' affects the vertical stretch or compression, 'b' affects the horizontal stretch or compression, 'c' shifts the graph left or right, and 'd' shifts it up or down.

Front

How does the value of 'a' affect the graph of an absolute value function?

Back

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

Front

What does the vertex of an absolute value function represent?

Back

The vertex is the highest or lowest point of the graph, depending on whether it opens upwards or downwards, and it represents the minimum or maximum value of the function.

Front

How do you find the vertex of the function f(x) = a|bx + c| + d?

Back

The vertex can be found at the point (-c/b, d). This is the point where the function changes direction.

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 that opens upwards?

Back

The range is [d, ∞) where 'd' is the y-coordinate of the vertex.

Front

What is the range of an absolute value function that opens downwards?

Back

The range is (-∞, d] where 'd' is the y-coordinate of the vertex.

Front

How do you determine the maximum or minimum value of an absolute value function?

Back

The maximum or minimum value is found at the vertex of the function. If the function opens upwards, the vertex gives the minimum value; if it opens downwards, it gives the maximum value.

Front

What does the expression |x - h| represent in the context of graphing?

Back

The expression |x - h| represents a horizontal shift of the basic absolute value function |x| to the right by 'h' units.