91Ó°ÊÓ

In your own words, describe how to find the distance between two points in the rectangular coordinate system.

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=x^{2}-1 $$

Begin by graphing the square root function, \(f(x)-\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$ h(x)-\sqrt{x+2}-2 $$

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=\sqrt[3]{2-x} $$

What is a circle? Without using variables, describe how the definition of a circle can be used to obtain a form of its equation.

Give an example of a circle's equation in standard form. Describe how to find the center and radius for this circle.

Begin by graphing the square root function, \(f(x)-\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$ h(x)-\sqrt{x+1}-1 $$

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=\frac{x^{3}}{2} $$

How is the standard form of a circle's equation obtained from its general form?

A cellphone company offers the following plans. Also given are the piecewise functions that model these plans. Use this information to solve. Plan \(A\) \(\cdot$$\$ 30\) per month buys 120 minutes. \(\cdot\) Additional time costs \(\$ 0.30\) per minute. $$C(t)=\left\\{\begin{array}{ll}30 & \text { if } 0 \leq t \leq 120 \\\30+0.30(t-120) & \text { if } t>120\end{array}\right.$$ Plan \(B\) \(\cdot \$ 40\) per month buys 200 minutes. \(\cdot\) Additional time costs \(\$ 0.30\) per minute. $$C(t)=\left\\{\begin{array}{ll}40 & \text { if } 0 \leq t \leq 200 \\\40+0.30(t-200) & \text { if } t>200\end{array}\right.$$ Simplify the algebraic expression in the second line of the piecewise function for plan A. Then use point-plotting to graph the function.