1a. Graph the function \(f(x) = x\).
b. Change the entry for \(f(x)\) to \(x \cdot x\).
c. Change the entry for \(f(x)\) to \(x \cdot x \cdot x\).
d. Change the entry for \(f(x)\) to \(x \cdot x \cdot x \cdot x\).
2a. Graph the function \(f(x) = x\).
b. Graph the function \(g(x) = x^{-1}\).
c. Create a table of values for the aforementioned \(f(x)\) and \(g(x)\). Include values of these functions for the following values of \(x\): \(1\), \(-1\), \(2\), \(-2\), \(3\), and \(-3\).
d. Are there any values of \(x\) for which \(g(x)\) is undefined?
3a. Graph the function \(f(x) = x^{-1}\).
b. Change the entry for \(f(x)\) to \(x^{-1} \cdot x^{-1}\).
c. Change the entry for \(f(x)\) to \(x^{-1} \cdot x^{-1} \cdot x^{-1}\).
d. Are there any values of \(x\) for which \(g(x)\) is undefined?
(i) Try adding coefficients to this expression to see if your answer for part d changes.
(ii) Try adding terms with positive exponents to this expression to see if your answer for part d changes.