Chapter 3

\(1-6\) Find \(f+g, f-g, f g,\) and \(f / g\) and their domains. $$ f(x)=x-3, \quad g(x)=x^{2} $$

Sketch the graph of the function by first making a table of values. $$ f(x)=2 $$

\(1-4\) . The graph of a quadratic function \(f\) is given. (a) Find the coordinates of the vertex. (b) Find the maximum or minimum value of \(f\) $$ f(x)=-x^{2}+6 x-5 $$

Express the rule in function notation. For example, the rule square, then subtract 5 is expressed as the function \(f(x)=x^{2}-5 .\) Add \(3,\) then multiply by 2

\(1-6\) Find \(f+g, f-g, f g,\) and \(f / g\) and their domains. $$ f(x)=x^{2}+2 x, \quad g(x)=3 x^{2}-1 $$

Sketch the graph of the function by first making a table of values. $$ f(x)=-3 $$

\(1-4\) . The graph of a quadratic function \(f\) is given. $$ f(x)=-\frac{1}{2} x^{2}-2 x+6 $$

Express the rule in function notation. For example, the rule square, then subtract 5 is expressed as the function \(f(x)=x^{2}-5 .\) Divide by \(7,\) then subtract 4

\(1-6\) Find \(f+g, f-g, f g,\) and \(f / g\) and their domains. $$ f(x)=\sqrt{4-x^{2}}, \quad g(x)=\sqrt{1+x} $$

Sketch the graph of the function by first making a table of values. $$ f(x)=2 x-4 $$

Express the rule in function notation. For example, the rule square, then subtract 5 is expressed as the function \(f(x)=x^{2}-5 .\) Subtract \(5,\) then square

\(1-6\) Find \(f+g, f-g, f g,\) and \(f / g\) and their domains. $$ f(x)=\sqrt{9-x^{2}}, \quad g(x)=\sqrt{x^{2}-4} $$

Sketch the graph of the function by first making a table of values. $$ f(x)=6-3 x $$

\(1-4\) . The graph of a quadratic function \(f\) is given. (a) Find the coordinates of the vertex. (b) Find the maximum or minimum value of \(f\) $$ f(x)=3 x^{2}+6 x-1 $$

1–10 ? Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. (a) \(y=-f(x) \quad\) (b) \(y=f(-x)\)

Express the rule in function notation. For example, the rule square, then subtract 5 is expressed as the function \(f(x)=x^{2}-5 .\) Take the square root, add \(8,\) then multiply by \(\frac{1}{3}\)

\(1-6\) Find \(f+g, f-g, f g,\) and \(f / g\) and their domains. $$ f(x)=\frac{2}{x}, \quad g(x)=\frac{4}{x+4} $$

Sketch the graph of the function by first making a table of values. $$ f(x)=-x+3, \quad-3 \leq x \leq 3 $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=x^{2}-6 x $$

\(5-12\) . A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) . (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$ f(x)=x^{2 / 5} $$

Express the function (or rule) in words. $$ f(x)=\frac{x-4}{3} $$

\(1-6\) Find \(f+g, f-g, f g,\) and \(f / g\) and their domains. $$ f(x)=\frac{2}{x+1}, \quad g(x)=\frac{x}{x+1} $$

Sketch the graph of the function by first making a table of values. $$ f(x)=\frac{x-3}{2}, \quad 0 \leq x \leq 5 $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=x^{2}+8 x $$

1–10 ? Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. (a) \(y=-f(x)+5 \quad\) (b) \(y=3 f(x)-5\)

\(5-12\) . A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) . (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$ f(x)=4-x^{2 / 3} $$

Express the function (or rule) in words. $$ g(x)=\frac{x}{3}-4 $$

\(7-10\) Find the domain of the function. $$ f(x)=\sqrt{x}+\sqrt{1-x} $$

Sketch the graph of the function by first making a table of values. $$ f(x)=-x^{2} $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=2 x^{2}+6 x $$

Determine whether the function is one-to-one. \(f(x)=-2 x+4\)

\(5-12\) . A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) . (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$ f(x)=x^{2}-5 x $$

Express the function (or rule) in words. $$ h(x)=x^{2}+2 $$

\(7-10\) Find the domain of the function. $$ g(x)=\sqrt{x+1}-\frac{1}{x} $$

Sketch the graph of the function by first making a table of values. $$ f(x)=x^{2}-4 $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=-x^{2}+10 x $$

Determine whether the function is one-to-one. \(f(x)=3 x-2\)

\(5-12\) . A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) . (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$ f(x)=x^{3}-4 x $$

Express the function (or rule) in words. $$ k(x)=\sqrt{x+2} $$

\(7-10\) Find the domain of the function. $$ h(x)=(x-3)^{-1 / 4} $$

Sketch the graph of the function by first making a table of values. $$ g(x)=x^{3}-8 $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=x^{2}+4 x+3 $$

1–10 ? Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. (a) \(y=f(4 x) \quad\) (b) \(y=f\left(\frac{1}{4} x\right)\)

Determine whether the function is one-to-one. \(g(x)=\sqrt{x}\)

\(5-12\) . A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) . (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$ f(x)=2 x^{3}-3 x^{2}-12 x $$

Draw a machine diagram for the function. $$ f(x)=\sqrt{x-1} $$

\(7-10\) Find the domain of the function. $$ k(x)=\frac{\sqrt{x+3}}{x-1} $$

Sketch the graph of the function by first making a table of values. $$ g(x)=4 x^{2}-x^{4} $$

\(5-18=\) A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x-\) and \(y\) -intercept(s). (c) Sketch its graph. $$ f(x)=x^{2}-2 x+2 $$

Determine whether the function is one-to-one. \(g(x)=|x|\)