Chapter 3

Exer. 1-2: Suppose \(f\) is an even function and \(g\) is an odd function. Complete the table, if possible. $$ \begin{array}{|l|r|r|} \hline x & -2 & 2 \\ \hline f(x) & & 7 \\ \hline g(x) & & -6 \\ \hline \end{array} $$

Exer. 1-2: Find (a) \((f+g)(3)\) (b) \((f-g)(3)\) (c) \((f g)(3)\) (d) \((f / g)(3)\) $$ f(x)=x+3, \quad g(x)=x^{2} $$

If \(f(x)=-x^{2}-x-4\), find \(f(-2), f(0)\), and \(f(4)\).

Exer. 1-6: Sketch the line through \(A\) and \(B\), and find its slope \(m\). $$ A(-3,2), \quad B(5,-4) $$

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=2 x-3 $$

Plot the points \(A(5,-2), B(-5,-2), C(5,2), D(-5,2)\), \(E(3,0)\), and \(F(0,3)\) on a coordinate plane.

Exer. 1-2: Suppose \(f\) is an even function and \(g\) is an odd function. Complete the table, if possible. $$ \begin{array}{|c|c|c|} \hline x & -3 & 3 \\ \hline f(x) & & -5 \\ \hline g(x) & & 15 \\ \hline \end{array} $$

Exer. 1-2: Find (a) \((f+g)(3)\) (b) \((f-g)(3)\) (c) \((f g)(3)\) (d) \((f / g)(3)\) $$ f(x)=-x^{2}, \quad g(x)=2 x-1 $$

If \(f(x)=-x^{3}-x^{2}+3\), find \(f(-3), f(0)\), and \(f(2)\).

Exer. 1-6: Sketch the line through \(A\) and \(B\), and find its slope \(m\). $$ A(4,-1), \quad B(-6,-3) $$

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=3 x+2 $$

Plot the points \(A(-3,1), B(3,1), C(-2,-3), D(0,3)\), and \(E(2,-3)\) on a coordinate plane. Draw the line segments \(A B\), \(B C, C D, D E\), and \(E A\).

Exer. 3-12: Determine whether \(f\) is even, odd, or neither even nor odd. f(x)=5 x^{3}+2 x

Exer. 3-8: Find (a) \((f+g)(x),(f-g)(x),(f g)(x)\), and \((f / g)(x)\) (b) the domain of \(f+g, f-g\), and \(f g\) (c) the domain of \(f / g\) $$ f(x)=x^{2}+2, \quad g(x)=2 x^{2}-1 $$

Exer. 1-6: Sketch the line through \(A\) and \(B\), and find its slope \(m\). $$ A(2,5), \quad B(-7,5) $$

If \(f(x)=\sqrt{x-4}-3 x\), find \(f(4), f(8)\), and \(f(13)\)

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=-x+1 $$

Plot the points \(A(0,0), B(1,1), C(3,3), D(-1,-1)\), and \(E(-2,-2)\). Describe the set of all points of the form \((a, a)\), where \(a\) is a real number.

Exer. 3-12: Determine whether \(f\) is even, odd, or neither even nor odd. $$ f(x)=|x|-3 $$

Exer. 3-8: Find (a) \((f+g)(x),(f-g)(x),(f g)(x)\), and \((f / g)(x)\) (b) the domain of \(f+g, f-g\), and \(f g\) (c) the domain of \(f / g\) $$ f(x)=x^{2}+x, \quad g(x)=x^{2}-3 $$

If \(f(x)=\frac{x}{x-3}\), find \(f(-2), f(0)\), and \(f(3)\)

Exer. 1-6: Sketch the line through \(A\) and \(B\), and find its slope \(m\). $$ A(5,-1), \quad B(5,6) $$

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=-2 x-3 $$

Plot the points \(A(0,0), B(1,-1), C(3,-3), D(-1,1)\), and \(E(-3,3)\). Describe the set of all points of the form \((a,-a)\), where \(a\) is a real number.

Exer. 3-12: Determine whether \(f\) is even, odd, or neither even nor odd. $$ f(x)=3 x^{4}+2 x^{2}-5 $$

Exer. 3-8: Find (a) \((f+g)(x),(f-g)(x),(f g)(x)\), and \((f / g)(x)\) (b) the domain of \(f+g, f-g\), and \(f g\) (c) the domain of \(f / g\) $$ f(x)=\sqrt{x+5}, \quad g(x)=\sqrt{x+5} $$

Exer. 5-12: Express \(f(x)\) in the form \(a(x-h)^{2}+k\). $$ f(x)=-x^{2}-4 x-8 $$

Exer. 5-10: If \(a\) and \(h\) are real numbers, find (a) \(f(a)\) (b) \(f(-a)\) (c) \(-f(a)\) (d) \(f(a+h)\) (e) \(f(a)+f(h)\) (f) \(\frac{f(a+h)-f(a)}{h}\), if \(h \neq 0\) $$ f(x)=5 x-2 $$

Exer. 1-6: Sketch the line through \(A\) and \(B\), and find its slope \(m\). $$ A(-3,2), \quad B(-3,5) $$

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=-4 x^{2} $$

Exer. 3-12: Determine whether \(f\) is even, odd, or neither even nor odd. $$ f(x)=7 x^{5}-4 x^{3} $$

Exer. 3-8: Find (a) \((f+g)(x),(f-g)(x),(f g)(x)\), and \((f / g)(x)\) (b) the domain of \(f+g, f-g\), and \(f g\) (c) the domain of \(f / g\) $$ f(x)=\sqrt{3-2 x}, \quad g(x)=\sqrt{x+4} $$

Exer. 5-12: Express \(f(x)\) in the form \(a(x-h)^{2}+k\). $$ f(x)=x^{2}-6 x+11 $$

Exer. 5-10: If \(a\) and \(h\) are real numbers, find (a) \(f(a)\) (b) \(f(-a)\) (c) \(-f(a)\) (d) \(f(a+h)\) (e) \(f(a)+f(h)\) (f) \(\frac{f(a+h)-f(a)}{h}\), if \(h \neq 0\) $$ f(x)=3-4 x $$

Exer. 1-6: Sketch the line through \(A\) and \(B\), and find its slope \(m\). $$ A(4,-2), \quad B(-3,-2) $$

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=\frac{1}{3} x^{2} $$

Exer. 3-12: Determine whether \(f\) is even, odd, or neither even nor odd. $$ f(x)=8 x^{3}-3 x^{2} $$

Exer. 3-8: Find (a) \((f+g)(x),(f-g)(x),(f g)(x)\), and \((f / g)(x)\) (b) the domain of \(f+g, f-g\), and \(f g\) (c) the domain of \(f / g\) $$ f(x)=\frac{2 x}{x-4}, \quad g(x)=\frac{x}{x+5} $$

Exer. 5-12: Express \(f(x)\) in the form \(a(x-h)^{2}+k\). $$ f(x)=2 x^{2}-12 x+22 $$

Exer. 7-10: Use slopes to show that the points are vertices of the specified polygon. $$ A(-3,1), B(5,3), C(3,0), D(-5,-2) ; \quad \text { parallelogram } $$

Exer. 5-10: If \(a\) and \(h\) are real numbers, find (a) \(f(a)\) (b) \(f(-a)\) (c) \(-f(a)\) (d) \(f(a+h)\) (e) \(f(a)+f(h)\) (f) \(\frac{f(a+h)-f(a)}{h}\), if \(h \neq 0\) $$ f(x)=-x^{2}+4 $$

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=2 x^{2}-1 $$

Exer. 7-8: Describe the set of all points \(P(x, y)\) in a coordinate plane that satisfy the given condition. (a) \(x=-2\) (b) \(y=3\) (c) \(x \geq 0\) (d) \(x y>0\) (e) \(y<0\) (f) \(x=0\)

Exer. 3-12: Determine whether \(f\) is even, odd, or neither even nor odd. $$ f(x)=12 $$

Exer. 3-8: Find (a) \((f+g)(x),(f-g)(x),(f g)(x)\), and \((f / g)(x)\) (b) the domain of \(f+g, f-g\), and \(f g\) (c) the domain of \(f / g\) $$ f(x)=\frac{x}{x-2}, \quad g(x)=\frac{3 x}{x+4} $$

Exer. 5-12: Express \(f(x)\) in the form \(a(x-h)^{2}+k\). $$ f(x)=5 x^{2}+20 x+17 $$

Exer. 7-10: Use slopes to show that the points are vertices of the specified polygon. $$ A(2,3), B(5,-1), C(0,-6), D(-6,2) ; \quad \text { trapezoid } $$

Exer. 5-10: If \(a\) and \(h\) are real numbers, find (a) \(f(a)\) (b) \(f(-a)\) (c) \(-f(a)\) (d) \(f(a+h)\) (e) \(f(a)+f(h)\) (f) \(\frac{f(a+h)-f(a)}{h}\), if \(h \neq 0\) $$ f(x)=3-x^{2} $$

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=-x^{2}+2 $$

Exer. 7-8: Describe the set of all points \(P(x, y)\) in a coordinate plane that satisfy the given condition. (a) \(y=-2\) (b) \(x=-4\) (c) \(x / y<0\) (d) \(x y=0\) (e) \(y>1\) (f) \(y=0\)