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