91Ó°ÊÓ

Write a polynomial inequality whose solution set is \([-3,5]\)

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$(x-2)^{2} \leq 0$$

Write the equation of each parabola in standard form. Each group member should consult an almanac, newspaper, magazine, or the Internet to find data that initially increase and then decrease, or vice versa, and therefore can be modeled by a quadratic function. Group members should select the two sets of data that are most interesting and relevant. For each data set selected, a. Use the quadratic regression feature of a graphing utility to find the quadratic function that best fits the data. b. Use the equation of the quadratic function to make a prediction from the data. What circumstances might affect the accuracy of your prediction? c. Use the equation of the quadratic function to write and solve a problem involving maximizing or minimizing the function.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of a function with origin symmetry can rise to the left and rise to the right.

Involve writing a rational function that models a problem's conditions. A contractor is constructing the house shown in the figure. The cross section up to the roof is in the shape of a rectangle. The area of the rectangular floor of the house is 2500 square feet. Express the perimeter of the rectangular floor, \(P,\) as a function of the width of the rectangle, \(x .\)

Solve and graph the solution set on a number line: $$\frac{2 x-3}{4} \geq \frac{3 x}{4}+\frac{1}{2}$$ (Section P.9, Example 5 )

What is a rational function?

Use everyday language to describe the behavior of a graph near its vertical asymptote if \(f(x) \rightarrow \infty\) as \(x \rightarrow-2^{-}\) and \(f(x) \rightarrow-\infty\) as \(x \rightarrow-2^{+}\)

Describe how to graph a rational function.

If you are given the equation of a rational function, how can you tell if the graph has a slant asymptote? If it does, how do you find its equation?