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, denoted as f(x) = |x|, which outputs the non-negative value of x.

Front

What is the vertex of the absolute value function f(x) = |x|?

Back

The vertex of the absolute value function f(x) = |x| is at the point (0, 0).

Front

How does the graph of f(x) = |x - 2| shift compared to f(x) = |x|?

Back

The graph of f(x) = |x - 2| shifts 2 units to the right compared to f(x) = |x|.

Front

What effect does the equation f(x) = |x| + 3 have on the graph of f(x) = |x|?

Back

The equation f(x) = |x| + 3 shifts the graph of f(x) = |x| up by 3 units.

Front

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

Back

The negative sign reflects the graph of the absolute value function across the x-axis.

Front

What does the term 'transformation' refer to in the context of absolute value functions?

Back

Transformation refers to the changes made to the graph of the parent function, such as shifts, stretches, or reflections.

Front

If f(x) = |x + 1| - 4, where is the vertex located?

Back

The vertex is located at the point (-1, -4).

Front

What does the expression |x - 3| represent graphically?

Back

The expression |x - 3| represents a V-shaped graph that opens upwards with its vertex at the point (3, 0).

Front

How does the graph of f(x) = 2|x| compare to f(x) = |x|?

Back

The graph of f(x) = 2|x| is a vertical stretch of the graph of f(x) = |x|, making it narrower.

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 - h| + k, where (h, k) is the vertex.