91Ó°ÊÓ

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

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) \(g(f(3))\) $$ f(x)=3 x^{2}+4, \quad g(x)=5 x $$

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

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