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, denoted as f(x) = |x|.

Front

What is the vertex of the absolute value function f(x) = |x - h| + k?

Back

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

Front

Describe the effect of a negative sign in front of an absolute value function, such as f(x) = -|x|.

Back

It reflects the graph over the x-axis.

Front

What does the parameter 'k' represent in the function f(x) = |x| + k?

Back

The parameter 'k' represents a vertical shift of the graph; if k is positive, the graph shifts up, and if k is negative, it shifts down.

Front

What does the parameter 'h' represent in the function f(x) = |x - h|?

Back

The parameter 'h' represents a horizontal shift of the graph; if h is positive, the graph shifts right, and if h is negative, it shifts left.

Front

How does the coefficient 'a' in f(x) = a|x| affect the graph?

Back

If |a| > 1, the graph stretches vertically; if 0 < |a| < 1, it compresses vertically.

Front

What is the parent function of absolute value?

Back

The parent function is f(x) = |x|.

Front

What is the equation of the absolute value function that opens upwards?

Back

The equation is f(x) = a|x - h| + k, where a > 0.

Front

What is the equation of the absolute value function that opens downwards?

Back

The equation is f(x) = -a|x - h| + k, where a > 0.

Front

If f(x) = |x + 2|, what is the vertex of the graph?

Back

The vertex is (-2, 0).