Graphing Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an absolute value expression. It is defined as f(x) = |x|, which outputs the non-negative value of x.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx + c| + d, where a, b, c, and d are constants that affect the graph's shape and position.

Front

What does the vertex of an absolute value function represent?

Back

The vertex is the highest or lowest point of the graph, depending on whether the function opens upwards or downwards.

Front

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

Back

If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards. The larger the absolute value of 'a', the steeper the graph.

Front

What is the effect of 'c' in the function f(x) = |x + c|?

Back

The value of 'c' shifts the graph horizontally. If 'c' is positive, the graph shifts left; if negative, it shifts right.

Front

What does 'd' do in the function f(x) = |x| + d?

Back

The value of 'd' shifts the graph vertically. If 'd' is positive, the graph shifts up; if negative, it shifts down.

Front

What is the domain of an absolute value function?

Back

The domain of an absolute value function is all real numbers, or (-∞, ∞).

Front

What is the range of the function f(x) = |x|?

Back

The range is [0, ∞) because the absolute value is always non-negative.

Front

How do you find the vertex of the function f(x) = a|bx + c| + d?

Back

The vertex can be found at the point (-c/b, d) in the graph.

Front

What is the equation of the graph that opens downwards with vertex (2, 4)?

Back

The equation is f(x) = -|x - 2| + 4.