Question

use the graph of the function to find the domain and range of ( f ). (enter your answers using interval notation.)

use the graph to find the indicated function values.
(a) ( f(-1)= )
(b) ( f(0)= )
(c) ( f(1)= )
(d) ( f(2)= )

Explanation:

Step1: Find the domain

The domain of a function is the set of all \(x -\)values for which the function is defined. Looking at the graph, the \(x -\)values start from \(x=-2\) (open - circle) and end at \(x = 2\) (closed - circle). So, the domain is \([-2,2]\).

Step2: Find the range

The range of a function is the set of all \(y -\)values. The lowest \(y -\)value is \(y=-4\) and the highest \(y -\)value is \(y = 5\) (closed - circle). So, the range is \([-4,5]\).

Step3: Find \(f(-1)\)

To find \(f(-1)\), we look at the \(y -\)value when \(x=-1\). From the graph, when \(x =-1\), \(y=-3\). So, \(f(-1)=-3\).

Step4: Find \(f(0)\)

When \(x = 0\), from the graph, \(y=-3\). So, \(f(0)=-3\).

Step5: Find \(f(1)\)

When \(x = 1\), from the graph, \(y=-2\). So, \(f(1)=-2\).

Step6: Find \(f(2)\)

When \(x = 2\), from the graph (closed - circle), \(y = 5\). So, \(f(2)=5\).

Answer:

domain: \([-2,2]\)
range: \([-4,5]\)
(a) \(f(-1)=-3\)
(b) \(f(0)=-3\)
(c) \(f(1)=-2\)
(d) \(f(2)=5\)