Chapter 3

Exer. 15-16: Sketch the graph of the line through \(P\) for each value of \(m\). $$ P(-2,4) ; \quad m=1,-2,-\frac{1}{2} $$

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

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.) $$ f(x)=2 \sqrt{x}+c ; \quad c=-3,0,2 $$

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

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 \(f\). $$ f(x)=9 x^{2}+24 x+16 $$

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

Show that \(A(-4,2), B(1,4), C(3,-1)\), and \(D(-2,-3)\) are vertices of a square.

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.) $$ f(x)=\sqrt{9-x^{2}}+c ; \quad c=-3,0,2 $$

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

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 \(f\). $$ f(x)=-4 x^{2}+4 x-1 $$

Given \(A(-3,8)\), find the coordinates of the point \(B\) such that \(C(5,-10)\) is the midpoint of segment \(A B\).

Show that \(A(-4,-1), B(0,-2), C(6,1)\), and \(D(2,2)\) are vertices of a parallelogram.

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.) $$ f(x)=\frac{1}{2} \sqrt{x-c} ; \quad c=-2,0,3 $$

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

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 \(f\). $$ f(x)=x^{2}+4 x+9 $$

Exer. 19-20: Sketch the graphs of the lines on the same coordinate plane. $$ y=x+3, \quad y=x+1, \quad y=-x+1 $$

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

Given \(A(-3,8)\), find the coordinates of the point \(B\) such that \(C(5,-10)\) is the midpoint of segment \(A B\).

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.) $$ f(x)=-\frac{1}{2}(x-c)^{2} ; \quad c=-2,0,3 $$

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

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 \(f\). $$ f(x)=-3 x^{2}-6 x-6 $$

Exer. 19-20: Sketch the graphs of the lines on the same coordinate plane. $$ y=-2 x-1, \quad y=-2 x+3, \quad y=\frac{1}{2} x+3 $$

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

Given \(A(5,-8)\) and \(B(-6,2)\), find the point on segment \(A B\) that is three- fourths of the way from \(A\) to \(B\).

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.) $$ f(x)=c \sqrt{4-x^{2}} ; \quad c=-2,1,3 $$

Exer. 21-34: Find (a) \((f \circ g)(x)\) and the domain of \(f \circ g\) and (b) \((g \circ f)(x)\) and the domain of \(g \circ f\). $$ f(x)=x^{2}-3 x, \quad g(x)=\sqrt{x+2} $$

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 \(f\). $$ f(x)=-2 x^{2}+20 x-43 $$

Exer. 21-32: Find a general form of an equation of the line through the point \(A\) that satisfies the given condition. $$ A(5,-2) $$ (a) parallel to the \(y\)-axis (b) perpendicular to the \(y\)-axis

Exer. 21-32: Find the domain of \(f\). $$ f(x)=\sqrt{2 x+7} $$

Exer. 21-22: Prove that \(C\) is on the perpendicular bisector of segment \(A B\). $$ A(-4,-3), \quad B(6,1), \quad C(5,-11) $$

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.) $$ f(x)=(x+c)^{3} ; \quad c=-2,1,2 $$

Exer. 21-34: Find (a) \((f \circ g)(x)\) and the domain of \(f \circ g\) and (b) \((g \circ f)(x)\) and the domain of \(g \circ f\). $$ f(x)=\sqrt{x-15}, \quad g(x)=x^{2}+2 x $$

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 \(f\). $$ f(x)=2 x^{2}-4 x-11 $$

Exer. 21-32: Find the domain of \(f\). $$ f(x)=\sqrt{8-3 x} $$

Exer. 21-22: Prove that \(C\) is on the perpendicular bisector of segment \(A B\). $$ A(-3,2), \quad B(5,-4), \quad C(7,7) $$

Exer. 21-32: Find a general form of an equation of the line through the point \(A\) that satisfies the given condition. $$ A(-4,2) $$ (a) parallel to the \(x\)-axis (b) perpendicular to the \(x\)-axis

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.) $$ f(x)=c x^{3} ; \quad c=-\frac{1}{3}, 1,2 $$

Exer. 21-34: Find (a) \((f \circ g)(x)\) and the domain of \(f \circ g\) and (b) \((g \circ f)(x)\) and the domain of \(g \circ f\). $$ f(x)=x^{2}-4, \quad g(x)=\sqrt{3 x} $$

Exer. 21-32: Find a general form of an equation of the line through the point \(A\) that satisfies the given condition. $$ A(5,-3) ; \quad \text { slope }-4 $$

Exer. 21-32: Find the domain of \(f\). $$ f(x)=\sqrt{9-x^{2}} $$

Exer. 23-34: Sketch the graph of the circle or semicircle. $$ x^{2}+y^{2}=11 $$

Exer. 23-24: Find a formula that expresses the fact that an arbitrary point \(P(x, y)\) is on the perpendicular bisector \(l\) of segment \(A B\). $$ A(-4,-3), B(6,1) $$

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.) $$ f(x)=(c x)^{3}+1 ; \quad c=-1,1,4 $$

Exer. 21-34: Find (a) \((f \circ g)(x)\) and the domain of \(f \circ g\) and (b) \((g \circ f)(x)\) and the domain of \(g \circ f\). $$ f(x)=-x^{2}+1, \quad g(x)=\sqrt{x} $$

Exer. 21-32: Find a general form of an equation of the line through the point \(A\) that satisfies the given condition. $$ A(-1,4) ; \quad \text { slope } \frac{2}{3} $$

Exer. 21-32: Find the domain of \(f\). $$ f(x)=\sqrt{x^{2}-25} $$

Exer. 23-34: Sketch the graph of the circle or semicircle. $$ x^{2}+y^{2}=7 $$

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.) $$ f(x)=\sqrt{c x}-1 ; \quad c=-1, \frac{1}{9}, 4 $$

Exer. 21-34: Find (a) \((f \circ g)(x)\) and the domain of \(f \circ g\) and (b) \((g \circ f)(x)\) and the domain of \(g \circ f\). $$ f(x)=\sqrt{x-2}, \quad g(x)=\sqrt{x+5} $$

Exer. 21-32: Find a general form of an equation of the line through the point \(A\) that satisfies the given condition. $$ A(4,0) ; \quad \text { slope }-3 $$