Preview Activity 1.9.1.
Consider the functions \(f\) and \(g\) defined by the following table and the piecewise linear functions \(p\) and \(q\) defined by the following figure. Assume that the lines in the figure pass through whole number coordinates where they appear to do so; for example, \((2,2)\) lies on the graph of \(q\text{,}\) and \((3,-3)\) lies on the graph of \(p\text{.}\)
| \(x\) | 0 | 1 | 2 | 3 | 4 |
| \(f(x)\) | 5 | 10 | 15 | 20 | 25 |
| \(g(x)\) | 9 | 5 | 3 | 2 | 3 |
(a)
(b)
(c)
Are there any values of \(x\) for which \(r(x) = 0\text{?}\) If not, explain why; if so, determine all such values, with justification.
(d)
(e)
(f)
Are there any values of \(x\) in the interval \(-4 \le x \le 4\) for which \(s(x)\) is not defined? If not, explain why; if so, determine all such values, with justification.
