91Ó°ÊÓ

Suppose that a circle is tangent to both axes, is in the third quadrant, and has radius \(\sqrt{2} .\) Find the center-radius form of its equation.

Answer the following. Find the coordinates of the points that divide the line segment joining \((4,5)\) and \((10,14)\) into three equal parts.

Use a graphing calculator to solve each linear equation. $$2 x+7-x=4 x-2$$

Given functions \(f\) and \(g,\) find ( \(a\) ) \((f \circ g)(x)\) and its domain, and ( \(b\) ) \((g \circ f)(x)\) and its domain. See Examples 6 and 7 . $$f(x)=\sqrt{x}, \quad g(x)=x+3$$

An equation that defines \(y\) as a function of \(x\) is given. (a) Solve for \(y\) in terms of \(x\) and $$\text {replace \(y\) with the function notation } f(x) . \text { (b) Find } f(3)$$. $$y+2 x^{2}=3-x$$

Use a graphing calculator to solve each linear equation. $$4 x-3(4-2 x)=2(x-3)+6 x+2$$

An equation that defines \(y\) as a function of \(x\) is given. (a) Solve for \(y\) in terms of \(x\) and $$\text {replace \(y\) with the function notation } f(x) . \text { (b) Find } f(3)$$. $$y-3 x^{2}=2+x$$

Graph each function. $$y=(x+3)^{3}$$

Determine whether the three points are collinear by using slopes. $$(-1,4),(-2,-1),(1,14)$$

The table shows several points on the graph of a linear function. to see connections between the slope formula, the distance formula, the midpoint formula, and linear functions. $$\begin{array}{c|r} x & y \\ \hline 0 & -6 \\ 1 & -3 \\ 2 & 0 \\ 3 & 3 \\ 4 & 6 \\ 5 & 9 \\ 6 & 12 \end{array}$$ Use the second and third points in the table to find the slope of the line.