91Ó°ÊÓ

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. $$ y=10-f(x) $$

In Exercises \(11-20,\) use the pair of functions \(f\) and \(g\) to find the domain of the indicated function then find and simplify an expression for it. -\((f+g)(x)\) -\((f-g)(x)\) -\((f g)(x)\) -\(\left(\frac{f}{g}\right)(x)\) $$f(x)=2 x+1 \text { and } g(x)=x-2$$

Use the given function \(f\) to find and simplify the following: \- \(f(3)\) \- \(f(4 x)\) \- \(f(x-4)\) \- \(f(-1)\) \- \(4 f(x)\) -\(f(x)-4\) \- \(f\left(\frac{3}{2}\right)\) \- \(f(-x)\) \- \(f\left(x^{2}\right)\) $$f(x)=2 x+1$$

Write the set using interval notation. $$ \\{x \mid x \neq 0,2\\} $$

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

Write the set using interval notation. $$ \\{x \mid x \neq 2,-2\\} $$

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. $$ y=3 f(2 x)-1 $$

Use the given function \(f\) to find and simplify the following: \- \(f(3)\) \- \(f(4 x)\) \- \(f(x-4)\) \- \(f(-1)\) \- \(4 f(x)\) -\(f(x)-4\) \- \(f\left(\frac{3}{2}\right)\) \- \(f(-x)\) \- \(f\left(x^{2}\right)\) $$f(x)=3-4 x$$

Determine whether or not the relation represents \(y\) as a function of \(x .\) Find the domain and range of those relations which are functions. $$ \left\\{\left(x^{2}, x\right) \mid x \text { is a real number }\right\\} $$

In Exercises \(11-20,\) use the pair of functions \(f\) and \(g\) to find the domain of the indicated function then find and simplify an expression for it. -\((f+g)(x)\) -\((f-g)(x)\) -\((f g)(x)\) -\(\left(\frac{f}{g}\right)(x)\) $$f(x)=1-4 x \text { and } g(x)=2 x-1$$