91Ó°ÊÓ

Determine whether the three points are collinear by using slopes. $$(-1,-3),(-5,12),(1,-11)$$

Determine whether the three points are collinear by using slopes. $$(0,9),(-3,-7),(2,19)$$

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. $$\begin{array}{c|r} x & y \\ \hline 0 & -6 \\ 1 & -3 \\ 2 & 0 \\ 3 & 3 \\ 4 & 6 \\ 5 & 9 \\ 6 & 12 \end{array}$$ Find the distance between the second and fourth points in the table.

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. $$\begin{array}{c|r} x & y \\ \hline 0 & -6 \\ 1 & -3 \\ 2 & 0 \\ 3 & 3 \\ 4 & 6 \\ 5 & 9 \\ 6 & 12 \end{array}$$ Find the midpoint of the segment joining \((0,-6)\) and \((6,12) .\) Compare your answer to the middle entry in the table. What do you notice?

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. $$\begin{array}{c|r} x & y \\ \hline 0 & -6 \\ 1 & -3 \\ 2 & 0 \\ 3 & 3 \\ 4 & 6 \\ 5 & 9 \\ 6 & 12 \end{array}$$ If the table were set up to show an \(x\) -value of \(4.5,\) what would be the corresponding y-value?

Find functions \(f\) and \(g\) such that \((f \circ g)(x)=h(x) .\) (There are many possible ways to do this.) See Example 9 $$h(x)=(2 x-3)^{3}$$

Find the function \(g(x)=a x+b\) whose graph can be obtained by translating the graph of \(f(x)=2 x+5\) up 2 units and to the left 3 units.

Solve each problem. An oil well off the Gulf Coast is leaking, with the leak spreading oil over the water's surface as a circle. At any time \(t,\) in minutes, after the beginning of the leak, the radius of the circular oil slick on the surface is \(r(t)=4 t\) feet. Let \(\mathscr{A}(r)=\pi r^{2}\) represent the area of a circle of radius \(r\) (a) Find \((\mathscr{A} \circ r)(t)\) (b) Interpret \((\mathscr{A} \circ r)(t)\) (c) What is the area of the oil slick after 3 min?