91Ó°ÊÓ

In Exercises \(1-12\), sketch the graph of the given function. State the domain of the function, identify any intercepts and test for symmetry. $$ f(x)=x^{3} $$

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

Find the indicated intersection or union and simplify if possible. Express your answers in interval notation. $$ (-\infty, 5] \cap[5,8) $$

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

Graph the given relation. $$ \\{(x,-2) \mid x>-4\\} $$

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) take the square root; (2) subtract \(13 ;(3)\) make the quantity the denominator of a fraction with numerator 4 .

Determine whether or not the relation represents \(y\) as a function of \(x .\) Find the domain and range of those relations which are functions. $$ \\{(1,0),(2,1),(4,2),(8,3),(16,4),(32,5), \ldots\\} $$

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

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) subtract \(13 ;\) (2) take the square root; (3) make the quantity the denominator of a fraction with numerator 4 .

Graph the given relation. $$ \\{(x, 3) \mid x \leq 4\\} $$