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Cumulative Review Exercises Chapters P–7

Let $f (x) = x^{2} -^{} 3 x + 2 .$ $f (x) = x^{2} -^{} 3 x + 2 .$ Find $\frac{f (x + h) - f (x)}{h} .$ $\frac{f (x + h) - f (x)}{h} .$
Sketch the graph of $f (x) = \sqrt{x + 1} - 2 .$ $f (x) = \sqrt{x + 1} - 2 .$
Let $f (x) = 2 x - 3 .$ $f (x) = 2 x - 3 .$ Find the inverse function $f^{- 1}$ $f^{- 1}$ . Verify that $f (f^{- 1} (x)) = x .$ $f (f^{- 1} (x)) = x .$
Sketch the graph of $f (x) = {(\frac{1}{2})}^{x + 2} .$ $f (x) = {(\frac{1}{2})}^{x + 2} .$
Solve the equation $\log_{5} (x - 1) + \log_{5} (x - 2) = 3 \log_{5} \sqrt[3]{6} .$ $\log_{5} (x - 1) + \log_{5} (x - 2) = 3 \log_{5} \sqrt[3]{6} .$
Express

$\log_{a} \sqrt[3]{x \sqrt{y z}}$ $\log_{a} \sqrt[3]{x \sqrt{y z}}$

in terms of logarithms of x, y, and z.
Solve the inequality $\frac{x}{x - 2} \geq 1 .$ $\frac{x}{x - 2} \geq 1 .$
The current I in an electric circuit is given by

$I = \frac{V}{R} (1 - e^{- 0.3 t}) .$ $I = \frac{V}{R} (1 - e^{- 0.3 t}) .$

Use natural logarithms to solve for t.

In Problems 9–12, solve each system of equations.

${\begin{array}{l} 1.4 x & - & 0.5 y & = & 1.3 \\ 0.4 x & + & 1.1 y & = & 4.1 \end{array}$ ${\begin{array}{l} 1.4 x & - & 0.5 y & = & 1.3 \\ 0.4 x & + & 1.1 y & = & 4.1 \end{array}$
${\begin{array}{rrrrrrl} 2 x & + & y & - & 4 z & = & 3 \\ x & - & 2 y & + & 3 z & = & 4 \\ - 3 x & + & 4 y & - & z & = & - 2 \end{array}$ ${\begin{array}{rrrrrrl} 2 x & + & y & - & 4 z & = & 3 \\ x & - & 2 y & + & 3 z & = & 4 \\ - 3 x & + & 4 y & - & z & = & - 2 \end{array}$
${\begin{array}{rcl} y & = & 2 - \log x \\ y - \log (x + 3) & = & 1 \end{array}$ ${\begin{array}{rcl} y & = & 2 - \log x \\ y - \log (x + 3) & = & 1 \end{array}$
${\begin{array}{rcl} y & = & x^{2} - 1 \\ 3 x^{2} + 8 y^{2} & = & 8 \end{array}$ ${\begin{array}{rcl} y & = & x^{2} - 1 \\ 3 x^{2} + 8 y^{2} & = & 8 \end{array}$
Find the determinant of the matrix $[\begin{array}{r} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array}]$ $[\begin{array}{r} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array}]$ .
Use Cramer’s Rule to solve the system of equations.

${\begin{array}{r} 2 x - 3 y & = & - 4 \\ 5 x + 7 y & = & 1 \end{array}$ ${\begin{array}{r} 2 x - 3 y & = & - 4 \\ 5 x + 7 y & = & 1 \end{array}$
Find the inverse of the matrix $A = [\begin{array}{r} 3 & - 2 \\ - 5 & 4 \end{array}]$ $A = [\begin{array}{r} 3 & - 2 \\ - 5 & 4 \end{array}]$ .
Find an equation of the line that passes through the point of intersection of the lines $x + 2 y - 3 = 0$ $x + 2 y - 3 = 0$ and $3 x + 4 y - 5 = 0$ $3 x + 4 y - 5 = 0$ and that is perpendicular to the line $x - 3 y + 5 = 0 .$ $x - 3 y + 5 = 0 .$ Write your answer in slope–intercept form.
Solve the equation $2 x^{4} - 5 x^{2} + 3 = 0 .$ $2 x^{4} - 5 x^{2} + 3 = 0 .$

In Problems 18–20, an equation of a conic section is given. Identify the conic and sketch its graph.

$x^{2} -^{} y^{2} = - 4$ $x^{2} -^{} y^{2} = - 4$
$9 x^{2} + 9 y^{2} = 144$ $9 x^{2} + 9 y^{2} = 144$
Sketch the graph of the rational function $f (x) = \frac{x}{x^{2} -^{} 16} .$ $f (x) = \frac{x}{x^{2} -^{} 16} .$

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Table of Contents for Cumulative Review Exercises Chapters P&#8211;7

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Table of Contents for
Cumulative Review Exercises Chapters P–7