Preview Activity 1.2.1.
Suppose that \(g\) is the function given by the graph below. Use the graph in Figure 1.2.1 to answer each of the following questions.
(a)
Determine the values \(g(-2)\text{,}\) \(g(-1)\text{,}\) \(g(0)\text{,}\) \(g(1)\text{,}\) and \(g(2)\text{,}\) if defined. If the function value is not defined, explain what feature of the graph tells you this.
(b)
For each of the values \(a = -1\text{,}\) \(a = 0\text{,}\) and \(a = 2\text{,}\) complete the following sentence: “As \(x\) gets closer and closer (but not equal) to \(a\text{,}\) \(g(x)\) gets as close as we want to .”
(c)
What happens as \(x\) gets closer and closer (but not equal) to \(a = 1\text{?}\) Does the function \(g(x)\) get as close as we would like to a single value?
