Chapter 3

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

Exer. 9-10: Find (a) \((f \circ g)(x)\) (b) \((g \circ f)(x)\) (c) \((f \circ f)(x)\) (d) \((g \circ g)(x)\) $$ f(x)=2 x-1, \quad g(x)=-x^{2} $$

Exer. 5-12: Express \(f(x)\) in the form \(a(x-h)^{2}+k\). $$ f(x)=-3 x^{2}-6 x-5 $$

Exer. 7-10: Use slopes to show that the points are vertices of the specified polygon. $$ A(6,15), B(11,12), C(-1,-8), D(-6,-5) ; \text { rectangle } $$

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 \(h \neq 0\) $$ f(x)=x^{2}-x+3 $$

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

Exer. 9-14: (a) Find the distance \(d(A, B)\) between \(A\) and \(B\). (b) Find the midpoint of the segment \(A B\). $$ A(4,-3), \quad B(6,2) $$

Exer. 3-12: Determine whether \(f\) is even, odd, or neither even nor odd. $$ f(x)=3 x^{2}-5 x+1 $$

Exer. 9-10: Find (a) \((f \circ g)(x)\) (b) \((g \circ f)(x)\) (c) \((f \circ f)(x)\) (d) \((g \circ g)(x)\) $$ f(x)=3 x^{2}, \quad g(x)=x-1 $$

Exer. 5-12: Express \(f(x)\) in the form \(a(x-h)^{2}+k\). $$ f(x)=-4 x^{2}+16 x-13 $$

Exer. 7-10: Use slopes to show that the points are vertices of the specified polygon. $$ A(1,4), B(6,-4), C(-15,-6) ; \text { right triangle } $$

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 \(h \neq 0\) $$ f(x)=2 x^{2}+3 x-7 $$

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

Exer. 9-14: (a) Find the distance \(d(A, B)\) between \(A\) and \(B\). (b) Find the midpoint of the segment \(A B\). $$ A(-2,-5), \quad B(4,6) $$

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

Exer. 11-20: Find (a) \((f \circ g)(x)\) (b) \((g \circ f)(x)\) (c) \(f(g(-2))\) (d) \(g(f(3))\) $$ f(x)=2 x-5, \quad g(x)=3 x+7 $$

Exer. 5-12: Express \(f(x)\) in the form \(a(x-h)^{2}+k\). $$ f(x)=-\frac{3}{4} x^{2}+9 x-34 $$

Exer. 7-10: Use slopes to show that the points are vertices of the specified polygon. If three consecutive vertices of a parallelogram are \(A(-1,-3), B(4,2)\), and \(C(-7,5)\), find the fourth vertex.

Exer. 11-14: If \(a\) is a positive real number, find (a) \(g\left(\frac{1}{a}\right)\) (b) \(\frac{1}{g(a)}\) (c) \(g(\sqrt{a})\) (d) \(\sqrt{g(a)}\) $$ g(x)=4 x^{2} $$

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

Exer. 9-14: (a) Find the distance \(d(A, B)\) between \(A\) and \(B\). (b) Find the midpoint of the segment \(A B\). $$ A(-5,0), \quad B(-2,-2) $$

Exer. 3-12: Determine whether \(f\) is even, odd, or neither even nor odd. $$ f(x)=x^{3}-\frac{1}{x} $$

Exer. 11-20: Find (a) \((f \circ g)(x)\) (b) \((g \circ f)(x)\) (c) \(f(g(-2))\) (d) \(g(f(3))\) $$ f(x)=5 x+2, \quad g(x)=6 x-1 $$

Exer. 5-12: Express \(f(x)\) in the form \(a(x-h)^{2}+k\). $$ f(x)=\frac{2}{5} x^{2}-\frac{12}{5} x+\frac{23}{5} $$

Exer. 7-10: Use slopes to show that the points are vertices of the specified polygon. Let \(A\left(x_{1}, y_{1}\right), B\left(x_{2}, y_{2}\right), C\left(x_{3}, y_{3}\right)\), and \(D\left(x_{4}, y_{4}\right)\) denote the vertices of an arbitrary quadrilateral. Show that the line segments joining midpoints of adjacent sides form a parallelogram.

Exer. 11-14: If \(a\) is a positive real number, find (a) \(g\left(\frac{1}{a}\right)\) (b) \(\frac{1}{g(a)}\) (c) \(g(\sqrt{a})\) (d) \(\sqrt{g(a)}\) $$ g(x)=2 x-5 $$

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

Exer. 9-14: (a) Find the distance \(d(A, B)\) between \(A\) and \(B\). (b) Find the midpoint of the segment \(A B\). $$ A(6,2), \quad B(6,-2) $$

Exer. 13-26: Sketch, on the same coordinate plane, the graphs of \(f\) for the given values of \(c\). (Make use of symmetry, shifting, stretching, compressing, or reflecting.) $$ f(x)=|x|+c ; \quad c=-3,1,3 $$

Exer. 11-20: Find (a) \((f \circ g)(x)\) (b) \((g \circ f)(x)\) (c) \(f(g(-2))\) (d) \(g(f(3))\) $$ f(x)=3 x^{2}+4, \quad g(x)=5 x $$

Exer. 13-22: (a) Use the quadratic formula to find the zeros of \(f\). (b) Find the maximum or minimum value of \(f(x)\). (c) Sketch the graph of \(f\). $$ f(x)=x^{2}-4 x $$

Exer. 13-14: Sketch the graph of \(y=m x\) for the given values of \(m\). $$ m=3,-2, \frac{2}{3},-\frac{1}{4} $$

Exer. 11-14: If \(a\) is a positive real number, find (a) \(g\left(\frac{1}{a}\right)\) (b) \(\frac{1}{g(a)}\) (c) \(g(\sqrt{a})\) (d) \(\sqrt{g(a)}\) $$ g(x)=\frac{2 x}{x^{2}+1} $$

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

Exer. 9-14: (a) Find the distance \(d(A, B)\) between \(A\) and \(B\). (b) Find the midpoint of the segment \(A B\). $$ A(7,-3), \quad B(3,-3) $$

Exer. 13-26: Sketch, on the same coordinate plane, the graphs of \(f\) for the given values of \(c\). (Make use of symmetry, shifting, stretching, compressing, or reflecting.) $$ f(x)=|x-c| ; \quad c=-3,1,3 $$

Exer. 11-20: Find (a) \((f \circ g)(x)\) (b) \((g \circ f)(x)\) (c) \(f(g(-2))\) (d) \(g(f(3))\) $$ f(x)=3 x-1, \quad g(x)=4 x^{2} $$

Exer. 13-22: (a) Use the quadratic formula to find the zeros of \(f\). (b) Find the maximum or minimum value of \(f(x)\). (c) Sketch the graph of \(f\). $$ f(x)=-x^{2}-6 x $$

Exer. 13-14: Sketch the graph of \(y=m x\) for the given values of \(m\). $$ m=5,-3, \frac{1}{2},-\frac{1}{3} $$

Exer. 11-14: If \(a\) is a positive real number, find (a) \(g\left(\frac{1}{a}\right)\) (b) \(\frac{1}{g(a)}\) (c) \(g(\sqrt{a})\) (d) \(\sqrt{g(a)}\) $$ g(x)=\frac{x^{2}}{x+1} $$

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

Exer. 9-14: (a) Find the distance \(d(A, B)\) between \(A\) and \(B\). (b) Find the midpoint of the segment \(A B\). $$ A(-4,7), \quad B(0,-8) $$

Exer. 13-26: Sketch, on the same coordinate plane, the graphs of \(f\) for the given values of \(c\). (Make use of symmetry, shifting, stretching, compressing, or reflecting.) $$ f(x)=-x^{2}+c ; \quad c=-4,2,4 $$

Exer. 11-20: Find (a) \((f \circ g)(x)\) (b) \((g \circ f)(x)\) (c) \(f(g(-2))\) (d) \(g(f(3))\) $$ f(x)=2 x^{2}+3 x-4, \quad g(x)=2 x-1 $$

Exer. 13-22: (a) Use the quadratic formula to find the zeros of \(f\). (b) Find the maximum or minimum value of \(f(x)\). (c) Sketch the graph of \(f\). $$ f(x)=-12 x^{2}+11 x+15 $$

Exer. 15-16: Sketch the graph of the line through \(P\) for each value of \(m\). $$ P(3,1) ; \quad m=\frac{1}{2},-1,-\frac{1}{5} $$

Exer. 1-20: Sketch the graph of the equation, and label the \(x\) - and \(y\)-intercepts. $$ y=x^{3}-8 $$

Exer. 13-26: Sketch, on the same coordinate plane, the graphs of \(f\) for the given values of \(c\). (Make use of symmetry, shifting, stretching, compressing, or reflecting.) $$ f(x)=2 x^{2}-c ; \quad c=-4,2,4 $$

Exer. 11-20: Find (a) \((f \circ g)(x)\) (b) \((g \circ f)(x)\) (c) \(f(g(-2))\) (d) \(g(f(3))\) $$ f(x)=5 x-7, \quad g(x)=3 x^{2}-x+2 $$

Exer. 13-22: (a) Use the quadratic formula to find the zeros of \(f\). (b) Find the maximum or minimum value of \(f(x)\). (c) Sketch the graph of \(f\). $$ f(x)=6 x^{2}+7 x-24 $$