Chapter 8

\(y\) varies directly as the cube of \(x . y=k x^{3}\)

If \(f(x)=-2 x+5\), find \(f(3), f(5)\), and \(f(-2)\).

If \(f(x)=x^{2}-3 x-4\), find \(f(2), f(4)\), and \(f(-3)\). \(f(2)=-6 ; f(4)=0 ; f(-3)=14\)

If \(g(x)=-2 x^{2}+x-5\), find \(g(3), g(-1)\), and \(g(2 a)\).

\(s\) varies jointly as \(g\) and the square of \(t . \quad s=k g t^{2}\)

\(f(x)=2 x^{2}-3 x+5, \quad g(x)=x^{2}-4\)

\(f(x)=(x+3)^{4}+1\)

If \(g(x)=-x^{2}-4 x+6\), find \(g(0), g(5)\). and \(g(-a)\).

\(f(x)=-x^{2}+2\)

If \(h(x)=\frac{2}{3} x-\frac{3}{4}\), find \(h(3), h(4)\), and \(h\left(-\frac{1}{2}\right)\).

If \(h(x)=-\frac{1}{2} x+\frac{2}{3}\), find \(h(-2), h(6)\), and \(h\left(-\frac{2}{3}\right)\).

\(f(x)=\sqrt{x-1}, \quad g(x)=\sqrt{x}\)

If \(f(x)=\sqrt{2 x-1}\), find \(f(5), f\left(\frac{1}{2}\right)\), and \(f(23)\). \(f(5)=3 ; f\left(\frac{1}{2}\right)=0 ; f(23)=3 \sqrt{5}\)

\(l\) is directly proportional to \(r\) and \(t . \quad I=k r t\)

\(f(x)=(x-3)^{3}-1\)

If \(f(x)=\sqrt{3 x+2}\), find \(f\left(\frac{14}{3}\right), f(10)\), and \(f\left(-\frac{1}{3}\right)\).

If \(f(x)=-2 x+7\), find \(f(a), f(a+2)\), and \(f(a+h)\).

\(f(x)=-|x+2|\)

If \(f(x)=x^{2}-7 x\), find \(f(a), f(a-3)\), and \(f(a+h)\).

\(f(x)=-3\)

If \(f(x)=x^{2}-4 x+10\), find \(f(-a), f(a-4)\), and \(f(a+h)\).

If \(f(x)=2 x^{2}-x-1\), find \(f(-a), f(a+1)\), and \(f(a+h)\).

If \(f(x)=-x^{2}+3 x+5\), find \(f(-a), f(a+6)\), and \(f(-a+1)\).

\(f(x)=3, \quad g(x)=-3 x^{2}-1\)

If \(f(x)=-x^{2}-2 x-7\), find \(f(-a), f(-a-2)\), and \(f(a+7)\).

\(y\) varies jointly as \(x\) and \(z\) and inversely as \(w\), and \(y=\) 154 when \(x=6, z=11\), and \(w=3.7\)

If \(f(x)=\left\\{\begin{array}{rl}x & \text { for } x \geq 0 \\ x^{2} & \text { for } x<0\end{array}, \quad \begin{array}{l}\text { find } f(4), f(10), f(-3), \text { and } \\ f(-5)\end{array}\right.\)

\(V\) varies jointly as \(h\) and the square of \(r\), and \(V=1100\) when \(h=14\) and \(r=5 . \quad \frac{22}{7}\)

If \(f(x)=\left\\{\begin{array}{ll}3 x+2 & \text { for } x \geq 0 \\ 5 x-1 & \text { for } x<0\end{array}, \quad\right.\) find \(f(2), f(6), f(-1)\)

\(f(x)=x-|x|\)

Determine the linear function whose graph is a line with a slope of \(\frac{2}{3}\) and contains the point \((-1,3)\). $$ f(x)=\frac{2}{3} x+\frac{11}{3} $$

If \(f(x)=\left\\{\begin{array}{rl}2 x & \text { for } x \geq 0 \\ -2 x & \text { for } x<0\end{array}, \quad\right.\) find \(f(3), f(5), f(-3)\)

Determine the linear function whose graph is a line with a slope of \(-\frac{3}{5}\) and contains the point \((4,-5)\). \(f(x)=-\frac{3}{5} x-\frac{13}{5}\)

If \(f(x)=\left\\{\begin{array}{rll}2 & \text { for } x<0 & \\ x^{2}+1 & \text { for } 0 \leq x \leq 4, & \text { find } f(3), f(6) \\ -1 & \text { for } x>4 & f(0), \text { and } f(-3)\end{array}\right.\)

\(f(x)=\sqrt{x-2}, \quad g(x)=3 x-1\)

\(f(x)=-\left(x+\frac{5}{2}\right)^{2}+\frac{3}{2}\)

Determine the linear function whose graph is a line that contains the points \((-3,-1)\) and \((2,-6)\). $$ f(x)=-x-4 $$

If \(f(x)=\left\\{\begin{array}{rll}1 & \text { for } x>0 \\ 0 & \text { for }-1

If \(y\) is inversely proportional to the square of \(x\), and \(y=\frac{1}{8}\) when \(x=4\), find \(y\) when \(x=8 . \quad y=\frac{1}{32}\)

\(f(x)=\frac{1}{x}, \quad g(x)=\frac{1}{x^{2}}\)

Determine the linear function whose graph is a line that contains the points \((-2,-3)\) and \((4,3)\).

If \(V\) varies jointly as \(B\) and \(h\), and \(V=96\) when \(B=36\) and \(h=8\), find \(V\) when \(B=48\) and \(h=6 . \quad V=96\)

Determine the linear function whose graph is a line that is perpendicular to the line \(g(x)=5 x-2\) and contains the point \((6,3) . \quad f(x)=-\frac{1}{5} x+\frac{21}{5}\)

Determine the linear function whose graph is a line that is parallel to the line \(g(x)=-3 x-4\) and contains the point \((2,7) . \quad f(x)=-3 x+13\)

The time required for a car to travel a certain distance varies inversely as the rate at which it travels. If it takes 3 hours to travel the distance at 50 miles per hour, how long will it take at 30 miles per hour? 5 hours

\(f(x)=\sqrt{2-x}\)

The cost for burning a 75 -watt bulb is given by the function \(c(h)=0.0045 h\), where \(h\) represents the number of hours that the bulb burns. (a) How much does it cost to burn a 75-watt bulb for 3 hours per night for a 31 -day month? Express your answer to the nearest cent. \(\$ .42\) (b) Graph the function \(c(h)=0.0045 h\). (c) Use the graph in part (b) to approximate the cost of burning a 75 -watt bulb for 225 hours. (d) Use \(c(h)=0.0045 h\) to find the exact cost, to the nearest cent, of burning a 75 -watt bulb for 225 hours. \(\$ 1.01\)

The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 144 feet in 3 seconds, how far will it fall in 5 seconds? 400 feet

\(f(x)=\sqrt{x+1}, \quad g(x)=5 x-1\)

\(f(x)=\sqrt{-1-x}\)