91Ó°ÊÓ

Find an expression for \(f(x)\) and state its domain. \(f\) is a function that takes a real number \(x\) and performs the following three steps in the order given: (1) multiply by \(2 ;\) (2) add \(3 ;\) (3) take the square root.

In Exercises \(1-12\), sketch the graph of the given function. State the domain of the function, identify any intercepts and test for symmetry. $$ f(x)=4-x^{2} $$

Graph the given relation. $$ \left\\{\left(\frac{6}{k}, k\right) \mid k=\pm 1,\pm 2,\pm 3,\pm 4,\pm 5,\pm 6\right\\} $$

Determine whether or not the relation represents \(y\) as a function of \(x .\) Find the domain and range of those relations which are functions. $$ \\{(1,2),(4,4),(9,6),(16,8),(25,10),(36,12), \ldots\\} $$

Suppose (2,-3) is on the graph of \(y=f(x) .\) In Exercises \(1-18,\) use Theorem 1.7 to find a point on the graph of the given transformed function. $$ y=f(x-1) $$

Use the pair of functions \(f\) and \(g\) to find the following values if they exist. $$ \begin{array}{lll} \bullet(f+g)(2) & \bullet(f-g)(-1) & \bullet(g-f)(1) \\ \bullet(f g)\left(\frac{1}{2}\right) & \bullet\left(\frac{f}{g}\right)(0) & \bullet\left(\frac{g}{f}\right)(-2) \end{array} $$ $$ f(x)=2 x^{3} \text { and } g(x)=-x^{2}-2 x-3 $$

Find the indicated intersection or union and simplify if possible. Express your answers in interval notation. $$ (-\infty, 4] \cap(0, \infty) $$

In Exercises \(1-12\), sketch the graph of the given function. State the domain of the function, identify any intercepts and test for symmetry. $$ f(x)=2 $$

Graph the given relation. $$ \left\\{\left(n, 4-n^{2}\right) \mid n=0,\pm 1,\pm 2\right\\} $$

Determine whether or not the relation represents \(y\) as a function of \(x .\) Find the domain and range of those relations which are functions. $$ \\{(x, y) \mid x \text { is an odd integer, and } y \text { is an even integer }\\} $$