Chapter 3

Find the slope of each line. The line with equation \(4 x-3 y=-3\)

Let \(f(x)=-x^{3}+2 x-2\) and \(g(x)=\frac{2-x}{9+x}\) and find each value. $$ f(-1) $$

When evaluating \(\left|\begin{array}{rrr}4 & -1 & 2 \\ 6 & -1 & 0 \\ 1 & -3 & 4\end{array}\right|,\) why is it helpful to expand

Find the slope of each line. The line with equation \(y=3\)

Let \(f(x)=-x^{3}+2 x-2\) and \(g(x)=\frac{2-x}{9+x}\) and find each value. $$ f(10) $$

Explain how to find the minor of an element of a determinant.

Find the slope of each line. If the solution of the system \(\left\\{\begin{array}{l}A x+B y=-2 \\ B x-A y=-26\end{array} \text { is }(-3,5)\right.\) what are the values of the constants \(A\) and \(B ?\)

Let \(f(x)=-x^{3}+2 x-2\) and \(g(x)=\frac{2-x}{9+x}\) and find each value. $$ g(2) $$

Explain how to find \(x\) when solving a system of three linear equations in \(x, y,\) and \(z\) by Cramer's rule. Use the words coefficients and constants in your explanation.

Solve: \(\left\\{\begin{array}{l}2 a b-3 c d=1 \\ 3 a b-2 c d=1\end{array}\right.\) for \(a\) and \(c .\) Assume that \(b\) and \(d\) are nonzero constants.

Let \(f(x)=-x^{3}+2 x-2\) and \(g(x)=\frac{2-x}{9+x}\) and find each value. $$ g(-20) $$

Are the lines described by \(y=2 x-7\) and \(x-2 y=7\) perpendicular?

Find the domain of the function \(f(x)=\frac{1}{3 x+6}\)

Are the lines described by \(y=2 x-7\) and \(2 x-y=10\) parallel?

Find the domain of the function \(f(x)=|x|\)

How are the graphs of \(f(x)=x^{2}\) and \(g(x)=x^{2}-2\) related?

Write a dependent system of equations with a solution of \((-5,2)\)

Is the graph of a circle the graph of a function?

Write a system of three independent linear equations in two variables that has the solution \((-5,2)\)

The graph of a line passes through \((0,-3) .\) Is this the \(x\) -intercept or the \(y\) -intercept of the line?

What is the name of the function \(f(x)=|x| ?\)

For the function \(y=2 x^{2}+6 x+1,\) what is the independent variable and what is the dependent variable?

$$ \text { If } f(x)=x^{3}-x, \text { what is } f(-1) ? $$

Show that \(\left|\begin{array}{rrr}x & y & 1 \\ -2 & 3 & 1 \\ 3 & 5 & 1\end{array}\right|=0\) represents the equation of the line passing through \((-2,3)\) and \((3,5)\)

Show that \(\frac{1}{2}\left|\begin{array}{ccc}0 & 0 & 1 \\ 3 & 0 & 1 \\ 0 & 4 & 1\end{array}\right|\) represents the area of the triangle with vertices at \((0,0),(3,0),\) and \((0,4)\)