Chapter 1

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

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

Use the pair of functions \(f\) and \(g\) to find the following values if they exist. \- \((f+g)(2)\) \- \((f g)\left(\frac{1}{2}\right)\) -\((f-g)(-1)\) -\(\left(\frac{f}{g}\right)(0)\) -\((g-f)(1)\) -\(\left(\frac{g}{f}\right)(-2)\) $$f(x)=3 x+1 \text { and } g(x)=4-x$$

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) divide by 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. $$ \\{(-3,9),(-2,4),(-1,1),(0,0),(1,1),(2,4),(3,9)\\} $$

Graph the given relation. $$ \\{(-3,9),(-2,4),(-1,1),(0,0),(1,1),(2,4),(3,9)\\} $$

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

In Exercises \(1-12\), sketch the graph of the given function. State the domain of the function, identify any intercepts and test for symmetry. $$ f(x)=\frac{x-2}{3} $$

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

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) add \(3 ;\) (2) multiply by \(2 ;\) (3) divide by 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. $$ \\{(-3,0),(1,6),(2,-3),(4,2),(-5,6),(4,-9),(6,2)\\} $$

Graph the given relation. $$ \\{(-2,0),(-1,1),(-1,-1),(0,2),(0,-2),(1,3),(1,-3)\\} $$

Find the indicated intersection or union and simplify if possible. Express your answers in interval notation. $$ (-1,5] \cap[0,8) $$

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

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

Use the pair of functions \(f\) and \(g\) to find the following values if they exist. $$ \begin{array}{lll} \bullet(f+g)(2) & \bullet(f-g)(-1) & \bullet(g-f)(1) \\ \bullet(f g)\left(\frac{1}{2}\right) & \bullet\left(\frac{f}{g}\right)(0) & \bullet\left(\frac{g}{f}\right)(-2) \end{array} $$ $$ f(x)=x^{2}-x \text { and } g(x)=12-x^{2} $$

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) divide by \(4 ;(2)\) add \(3 ;\) (3) multiply by 2 .

Determine whether or not the relation represents \(y\) as a function of \(x .\) Find the domain and range of those relations which are functions. $$ \\{(-3,0),(-7,6),(5,5),(6,4),(4,9),(3,0)\\} $$

Graph the given relation. $$ \\{(m, 2 m) \mid m=0,\pm 1,\pm 2\\} $$

Find the indicated intersection or union and simplify if possible. Express your answers in interval notation. $$ (-1,1) \cup[0,6] $$

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

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

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 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.

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

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

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

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. $$ y=3 f(x) $$

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

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

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) add \(3 ;\) (2) multiply by \(2 ;\) (3) take the square root.

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

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

Find the indicated intersection or union and simplify if possible. Express your answers in interval notation. $$ (-\infty, 0) \cap[1,5] $$

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. $$ y=f(3 x) $$

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

Use the pair of functions \(f\) and \(g\) to find the following values if they exist. \- \((f+g)(2)\) \- \((f g)\left(\frac{1}{2}\right)\) -\((f-g)(-1)\) -\(\left(\frac{f}{g}\right)(0)\) -\((g-f)(1)\) -\(\left(\frac{g}{f}\right)(-2)\) $$f(x)=\sqrt{4-x} \text { and } g(x)=\sqrt{x+2}$$

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) add \(3 ;(2)\) take the square root; (3) multiply by 2 .

Determine whether or not the relation represents \(y\) as a function of \(x .\) Find the domain and range of those relations which are functions. $$ \\{(x, 1) \mid x \text { is an irrational number }\\} $$

Graph the given relation. $$ \\{(\sqrt{j}, j) \mid j=0,1,4,9\\} $$

Find the indicated intersection or union and simplify if possible. Express your answers in interval notation. $$ (-\infty, 0) \cup[1,5] $$

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

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

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. $$ \\{(1,0),(2,1),(4,2),(8,3),(16,4),(32,5), \ldots\\} $$

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

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

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

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

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