91Ó°ÊÓ

The graph of \(y=f(x)\) passes through the points (0,1) \((1,2),\) and \((2,3) .\) Find the corresponding points on the graph of \(y=f(x+2)-1\).

An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). (a) The table shows the volumes \(V\) (in cubic centimeters) of the box for various heights \(x\) (in centimeters). Use the table to estimate the maximum volume. $$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Height, } x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Volume, } V & 484 & 800 & 972 & 1024 & 980 & 864 \\ \hline \end{array}$$ (b) Plot the points \((x, V)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(V\) as a function of \(x\) ? (c) If \(V\) is a function of \(x\), write the function and determine its domain.

Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts \((a, 0)\) and \((0, b)\) is $$\frac{x}{a}+\frac{y}{b}=1, a \neq 0, b \neq 0.$$ \(x\) -intercept: (2,0) \(y\) -intercept: (0,3)

A balloon carrying a transmitter ascends vertically from a point 3000 feet from the receiving station. (a) Draw a diagram that gives a visual representation of the problem. Let \(h\) represent the height of the balloon and let \(d\) represent the distance between the balloon and the receiving station. (b) Write the height of the balloon as a function of \(d\). What is the domain of the function?

Determine whether the statement is true or false. Justify your answer. If the inverse function of \(f\) exists and the graph of \(f \mathrm{~h}\) a \(y\) -intercept, then the \(y\) -intercept of \(f\) is an \(x\) -intercep of \(f^{-1}\)

Identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that the slope appears visually correct- that is, so that parallel lines appear parallel and perpendicular lines appear to intersect at right angles. (a) \(y=x-8\) (b) \(y=x+1\) (c) \(y=-x+3\)

Determine if the situation could be represented by a one-to-one function. If so, write a statement that describes the inverse function. The depth of the tide \(d\) at a beach in terms of the time \(t\) over a 24 -hour period

You are given the dollar value of a product in 2010 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value \(V\) of the product in terms of the year \(t\). (Let \(t=10\) represent 2010.) $$ \text {2010 value} \quad \text {Rate}$$ $$\$ 156 \quad \$ 4.50$$ increase per year

Determine whether the statement is true or false. Justify your answer. The set of ordered pairs \(\\{(-8,-2),(-6,0),(-4,0),\) (-2,2),(0,4),(2,-2)\\} represents a function.

The value \(V\) of a molding machine \(t\) years after it is purchased is $$V=-4000 t+58,500, \quad 0 \leq t \leq 5$$ Explain what the \(V\) -intercept and the slope measure.