91Ó°ÊÓ

Show that \(y-y_{1}=m\left(x-x_{1}\right)\) simplifies to \(y=m x+b\) if the point \(\left(x_{1}, y_{1}\right)\) is the \(y\) -intercept \((0, b)\).

Use a calculator to evaluate each expression. Round answers to two decimal places. $$ 8^{2.7} $$

For each pair of functions \(f(x)\) and \(g(x)\), find a. \(f(g(x))\) b. \(g(f(x))\) and c. \(f(f(x))\) $$ f(x)=\sqrt{x} ; \quad g(x)=x^{3}-1 $$

Show that the linear equation \(\frac{x}{a}+\frac{y}{b}=1\) has \(x\) -intercept \((a, 0)\) and \(y\) -intercept \((0, b)\). (The \(x\) -intercept is the point where the line crosses the \(x\) -axis.)

Solve each equation by factoring or the Quadratic Formula, as appropriate. $$ 5 x^{2}+20=0 $$

Use a calculator to evaluate each expression. Round answers to two decimal places. $$ 5^{3.9} $$

53-62. Solve each equation using a graphing calculator. [Hint: Begin with the window \([-10,10]\) by \([-10,10]\) or another of your choice (see Useful Hint in Graphing Calculator Terminology following the Preface) and use ZERO, SOLVE, or TRACE and ZOOM IN.] (In Exercises 61 and 62 , round answers to two decimal places.) $$ x^{2}-x-20=0 $$

Use a graphing calculator to evaluate each expression. $$ \left[(0.1)^{0.1}\right]^{0.1} $$

For each pair of functions \(f(x)\) and \(g(x)\), find a. \(f(g(x))\) b. \(g(f(x))\) and c. \(f(f(x))\) $$ f(x)=\sqrt{x}-1 ; g(x)=x^{3}-x^{2} $$

a. Graph the lines \(y_{1}=-x, y_{2}=-2 x\), and \(y_{3}=-3 x\) on the window \([-5,5]\) by \([-5,5]\). Observe how the coefficient of \(x\) changes the slope of the line. b. Predict how the line \(y=-9 x\) would look, and then check your prediction by graphing it.