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 parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

How does the graph of f(x) = |x| look?

Back

The graph of f(x) = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

What transformation occurs when the function is f(x) = |x - h|?

Back

The graph of f(x) = |x - h| shifts the parent function to the right by h units if h > 0, and to the left by h units if h < 0.

Front

What transformation occurs when the function is f(x) = |x| + k?

Back

The graph of f(x) = |x| + k shifts the parent function up by k units if k > 0, and down by k units if k < 0.

Front

What does the negative sign in front of an absolute value function indicate?

Back

The negative sign indicates a reflection of the graph across the x-axis.

Front

What is the effect of a coefficient in front of the absolute value function, such as in f(x) = a|x|?

Back

The coefficient 'a' affects the vertical stretch or compression of the graph. If |a| > 1, the graph stretches; if 0 < |a| < 1, it compresses.

Front

What is the range of the function g(x) = |x - 6|?

Back

The range of g(x) = |x - 6| is [0, ∞) because the absolute value is always non-negative.

Front

How do you find the vertex of the function f(x) = a|x - h| + k?

Back

The vertex of the function f(x) = a|x - h| + k is at the point (h, k).

Front

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

Back

An absolute value function that opens downwards can be expressed as f(x) = -|x - h| + k.