91Ó°ÊÓ

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

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. $$ y=f(-x) $$

Write the set using interval notation. $$ \\{x \mid x \neq 5\\} $$

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 .

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. $$ y=f(x-3)+1 $$

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

Graph the given relation. $$ \\{(-1, y) \mid y>1\\} $$

Write the set using interval notation. $$ \\{x \mid x \neq-1\\} $$

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

In Exercises \(1-12\), sketch the graph of the given function. State the domain of the function, identify any intercepts and test for symmetry. $$ f(x)=\sqrt{5-x} $$