91Ó°ÊÓ

Determine whether the graph of each equation is symmetric with respect to the origin. $$y=-x^{3}$$

Find the range of \(f(x)=-2 x^{2}+5 x-1 .\) Determine the values of \(x\) in the domain of \(f\) for which \(f(x)=2\)

Graph each function. Insert solid circles or hollow circles where necessary to indicate the true nature of the function. $$g(x)=\left\\{\begin{array}{ll} -4, & \text { if } x \leq 0 \\ x^{2}-4, & \text { if } 01 \end{array}\right.$$

The height of an arch is given by the equation $$h(x)=-\frac{3}{64} x^{2}+27, \quad-24 \leq x \leq 24$$ where \(|x|\) is the horizontal distance in feet from the center of the arch. a. What is the maximum height of the arch? b. What is the height of the arch 10 feet to the right of center? c. How far from the center is the arch 8 feet tall? GRAPH CANT COPY

Soon after insect larvae are hatched, they must begin to search for food. The survival rate of the larvae depends on many factors, but the temperature of the environment is one of the most important. For a certain species of insect, a model of the number of larvae, \(N(T),\) that survive this searching period is given by $$N(T)=-0.6 T^{2}+32.1 T-350$$ where \(T\) is the temperature in degrees Celsius. a. At what temperature will the maximum number of larvae survive? Round to the nearest degree. b. What is the maximum number of surviving larvae? Round to the nearest whole number. c. Find the \(x\) -intercepts, to the nearest whole number, for the graph of this function. d. Write a sentence that describes the meaning of the \(x\) -intercepts in the context of this problem.

Solve each quadratic inequality. Use interval notation to write each solution set. $$x^{2}+7 x>0$$

Solve each quadratic inequality. Use interval notation to write each solution set. $$x^{2}-5 x \leq 0$$

Solve each quadratic inequality. Use interval notation to write each solution set. $$x^{2}+7 x+10<0$$

A piece of pottery is removed from a kiln and allowed to cool in a controlled environment. The temperature (in degrees Fahrenheit) of the pottery after it is removed from the kiln for various times (in minutes) is shown in the table below. $$\begin{array}{|c|c|}\hline \text { Time, min } & \text { Temperature, }^{\circ} \mathrm{F} \\\\\hline 15 & 2200 \\\\\hline 20 & 2150 \\\\\hline 30 & 2050 \\\\\hline 60 & 1750 \\\\\hline\end{array}$$ a. Find a linear model for the temperature of the pottery after \(t\) minutes. b. Explain the meaning of the slope of this line in the context of the problem. c. Assuming temperature continues to decrease at the same rate, what will be the temperature of the pottery in 3 hours?

Let \(f\) be a function such that \(f(-2)=5, f(0)=-2,\) and \(f(1)=0 .\) Give the coordinates of three points on the graph of a. \(y=f(x+3)\) b. \(y=f(x)+1\)