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Chapter 3: Problem 53
Explain how to decide whether a parabola opens upward or downward.
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In Exercises \(1-10\), determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=5 x^{2}+6 x^{3}$$
In Exercises \(35-50\) a. Use the Leading Coefficient Test to determine the graphs end behavior. b. Find \(x\) -intercepts by setting \(f(x)=0\) and solving the resulting polynomial equation. State whether the graph crosses the \(x\)-axis, or touches the \(x\)-axis and turns around, at each intercept. c. Find the \(y\) -intercept by setting \(x\) equal to 0 and computing \(f(0)\) d. Determine whether the graph has \(y\) -axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the fact that the maximum number of turning points of the graph is \(n-1\) to check whether it is drawn correctly. $$f(x)=x^{4}-6 x^{3}+9 x^{2}$$
Use a graphing utility to graph $$f(x)=\frac{x^{2}-4 x+3}{x-2} \quad \text { and} \quad g(x)=\frac{x^{2}-5 x+6}{x-2}$$ What differences do you observe between the graph of \(f\) and \(g ?\) How do you account for these differences?
In Exercises \(74-77\), use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function. $$f(x)=-x^{4}+8 x^{3}+4 x^{2}+2$$
The illumination from a light source varies inversely as the square of the distance from the light source. If you raise a lamp from 15 inches to 30 inches over your desk, what happens to the illumination?
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