Question

the graph of a function f is given. use the graph to estimate the following. (enter your answers using interval notation.)
(a) the domain and range of f.
domain
range
(b) the intervals on which f is increasing and on which f is decreasing.
increasing
decreasing

Explanation:

Step1: Determine the domain

The domain is the set of all \(x -\)values for which the function is defined. Looking at the graph, the left - most \(x -\)value is \(x=-1\) and the right - most \(x -\)value is \(x = 3\). So, the domain is \([-1,3]\).

Step2: Determine the range

The range is the set of all \(y -\)values. The lowest \(y -\)value (from the graph) is \(y=-2\) and the highest \(y -\)value is \(y = 2\). So, the range is \([-2,2]\).

Step3: Determine increasing intervals

A function \(y = f(x)\) is increasing when, as \(x\) increases, \(y\) also increases. From the graph, we can see that the function is increasing on the interval \([-1,1]\).

Step4: Determine decreasing intervals

A function \(y = f(x)\) is decreasing when, as \(x\) increases, \(y\) decreases. From the graph, the function is decreasing on the interval \([1,3]\).

Answer:

(a) Domain: \([-1,3]\), Range: \([-2,2]\)
(b) Increasing: \([-1,1]\), Decreasing: \([1,3]\)