Which of the following are graphs of functions? If the graph is that of a function, is it one-to-one? Four graphs are shown, labeled (a), (b), (c), and (d).

Let \(f(x) = \dfrac{\sqrt{x + 1}}{x}\). (a) Evaluate \(f(3)\), \(f(5)\), and \(f(a - 1)\). (b) Find the domain of \(f\).

A function \(f\) has the following verbal description: "Subtract 2, then cube the result." (a) Find a formula that expresses \(f\) algebraically. (b) Make a table of values of \(f\), for the inputs \(-1, 0, 1, 2, 3\), and \(4\). (c) Sketch a graph of \(f\), using the table of values from part (b) to help you. (d) How do we know that \(f\) has an inverse? Give a verbal description for \(f^{-1}\). (e) Find a formula that expresses \(f^{-1}\) algebraically.

A school fund-raising group sells chocolate bars to help finance a swimming pool for their physical education program. The group finds that when they set their price at \(x\) dollars per bar (where \(0 < x \leq 5\)), their total sales revenue (in dollars) is given by the function \(R(x) = -500x^2 + 3000x\). (a) Evaluate \(R(2)\) and \(R(4)\). What do these values represent? (b) Use a graphing calculator to draw a graph of \(R\). What does the graph tell us about what happens to revenue as the price increases from \(0\) to \(5\) dollars? (c) What is the maximum revenue, and at what price is it achieved?

Determine the average rate of change for the function \(f(t) = t^2 - 2t\) between \(t = 2\) and \(t = 5\).

(a) Sketch the graph of the function \(f(x) = x^3\). (b) Use part (a) to graph the function \(g(x) = (x - 1)^3 - 2\).

(a) How is the graph of \(y = f(x - 3) + 2\) obtained from the graph of \(f\)? (b) How is the graph of \(y = f(-x)\) obtained from the graph of \(f\)?

Let \(f(x) = \begin{cases} 1 - x & \quad \text{if } x \leq 1 \\ 2x + 1 & \quad \text{if } x > 1 \end{cases}\). (a) Evaluate \(f(-2)\) and \(f(1)\). (b) Sketch the graph of \(f\).

If \(f(x) = x^2 + 1\) and \(g(x) = x - 3\), find the following: (a) \(f \circ g\) (b) \(g \circ f\) (c) \(f(g(2))\) (d) \(g(f(2))\) (e) \(g \circ g \circ g\)

(a) If \(f(x) = 3 - x\), find the inverse function \(f^{-1}\). (b) Sketch the graphs of \(f\) and \(f^{-1}\) on the same coordinate axes.

The graph of a function \(f\) is given. (a) Find the domain and range of \(f\). (b) Sketch the graph of \(f^{-1}\). (c) Find the average rate of change of \(f\) between \(x = 2\) and \(x = 6\).

Let \(f(x) = 3x^4 - 14x^2 + 5x - 3\). (a) Draw the graph of \(f\) in an appropriate viewing rectangle. (b) Is \(f\) one-to-one? (c) Find the local maximum and minimum values of \(f\) and the values of \(x\) at which they occur. State each answer correct to two decimal places. (d) Use the graph to determine the range of \(f\). (e) Find the intervals on which \(f\) is increasing and on which \(f\) is decreasing.