4.3 HW Flashcard - Absolute Value Functions

Front

What is the definition of 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

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Back

The vertex is the point (h, k) where the graph changes direction.

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Back

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

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Back

The vertex is (-2, -3).

Front

How do you graph an absolute value function?

Back

1. Identify the vertex (h, k). 2. Determine the direction (upward or downward) based on 'a'. 3. Plot points on either side of the vertex using the absolute value formula. 4. Connect the points to form a V-shape.

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Back

Changing 'h' shifts the graph horizontally. If 'h' increases, the graph shifts to the right; if 'h' decreases, it shifts to the left.

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Back

Changing 'k' shifts the graph vertically. If 'k' increases, the graph shifts up; if 'k' decreases, it shifts down.

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Back

The vertex is (1, 5).

Front

How do you determine the y-intercept of an absolute value function?

Back

To find the y-intercept, set x = 0 in the function and solve for y.