Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that returns the non-negative value of a number, defined as f(x) = |x|, where |x| is the distance of x from 0 on the number line.

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|bx - c| + d, where a, b, c, and d are constants.

Front

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

Back

The parameter 'a' affects the vertical stretch or compression and the direction of the graph. If a > 0, the graph opens upwards; if a < 0, it opens downwards.

Front

What does the parameter 'd' represent in the absolute value function f(x) = a|bx - c| + d?

Back

The parameter 'd' represents a vertical shift of the graph. If d > 0, the graph shifts up; if d < 0, it shifts down.

Front

What is the effect of the parameter 'c' in the absolute value function?

Back

The parameter 'c' represents a horizontal shift. If c > 0, the graph shifts to the right; if c < 0, it shifts to the left.

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Back

7

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4

Front

What transformation does the function f(x) = |x| + 4 represent?

Back

The function f(x) = |x| + 4 represents a vertical shift upwards by 4 units.

Front

What transformation does the function f(x) = |x - 3| represent?

Back

The function f(x) = |x - 3| represents a horizontal shift to the right by 3 units.

Front

What is the vertex of the function f(x) = |x + 2| - 1?

Back

The vertex of the function f(x) = |x + 2| - 1 is at the point (-2, -1).