Question

constant
decrease
increase
range
domain

Explanation:

Step1: Determine the domain

The domain of a function is the set of all possible \(x -\)values. Looking at the graph, as \(x\) extends infinitely to the left and right (arrows on both ends of the graph), the \(x -\)values cover all real numbers. So, the domain is \((-\infty,\infty)\).

Step2: Determine the range

The range of a function is the set of all possible \(y -\)values. Observing the vertical spread of the graph, as the graph has no upper or lower bounds (it can go as low and as high as possible, indicated by the general trend and the nature of the continuous curve), the range is \((-\infty,\infty)\).

Step3: Determine intervals of increase

A function \(y = f(x)\) is increasing on an interval if, for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step4: Determine intervals of decrease

A function \(y = f(x)\) is decreasing on an interval if, for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step5: Determine constant intervals

A function \(y = f(x)\) is constant on an interval if, for any two points \(x_1\) and \(x_2\) in the interval, \(f(x_1)=f(x_2)\). There are no such intervals (where the \(y -\)value does not change with respect to \(x\)) on this graph.

Answer:

• Domain: \((-\infty,\infty)\)
• Range: \((-\infty,\infty)\)
• Increase: \((-\infty, - 3)\cup(3,\infty)\)
• Decrease: \((-3,3)\)
• Constant: None