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Determine the input that produces the largest or smallest output (whichever is apporpriate). State whether the output is largest or smallest. Complete the square where required.
Graph the quadratic equation. Specify the vertex, axis of symmetry, max or min value, and intercepts. Complete the square where needed.
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Find the linear function satisfying the given conditions. The x and y-inercepts of the inverse function are 5 and -1 respectively.
Explain why f^-1 is linear. In particular, what are the slope and y-intercept of the graph of y= f^-1(x)? What happens when m=0?
Investigate the inverse of a composite function. In parts b and c, which involve graphing be sure the same size unit and scale on both axes so that symmetry about the line y = x can be checked visua
Determine if exponential functions only model phenomena that grow, or if can they also model phenomena that decay.
Define a function n that represents the time in years since 2010 as a function of c, the concentration of the pollutant in Edmonton in ppm.
Because of corrosion, the surface area of the cable decreases at the rate of 750 in2 per year. Express the diameter d of the cable as a function of time t (in years). (Disregard corrosion at the end
Find the number (in millions) of women enrolled in U.S. colleges in the year 1998. Find the number (in millions) of men enrolled in U.S. colleges in the year 1998.
Angular speed is the rate at which the central angle is changing. Suppose a bicycle wheel with diameter 700 mm makes 30 revolutions in t seconds. Write an equation for the angular speed, v, as a fun
Calculate the maximum possible volume of the cylinder. It is probably best to take as your independent variable the height, or half the height, of the cylinder.
The company estimates that for each $25 increase in rent, 5 apartments will become unoccupied. What rent should be charged so that the company will receive the maximum monthly income?
A company sells running shoes to dealers at a rate of $40 per pair if fewer than 80 pairs are ordered. What size order will produce the maximum amount of money for the company?
A doorway has the shape of a parabolic arch and is 16 feet high at the center and 8 feet wide at the base. If a rectangular box 15 feet high must fit through the doorway, what is the maximum width t
Create your own graph of a function and find its domain ad range. State a real life situation that could be represented by your graph. Is your graph continuous? Explain.
Give an example of factoring using greatest common factor GCF, work the problem using GCF- show all steps. Consider the statement \((x+y)^{2}=x^{2}+y^{2}\).
What's the least number of computers must he sell in order to not lose money in his venture? This number of computers is called the 'break even' point.
A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides.
Find a mixture problem and demonstrate, step by step, how a system of equations can be used to solve your problem of choice.
A designer is creating various open-top boxes by cutting four equally-sized squares from the corners of a 21-cm by 32-cm sheet of cardboard. What is the maximum volume of the box?
Now, on your graphing calculartor plot y=sin(x)/sqrt(1-(cos(x))^2) both in its unsimplified form and in its simplified form. Does the graph apperar the same?
Determine the total length of frame needed for a window with a base length of 4 feet. Round your answer to the nearest hundredth of a foot.
Find the rate at which the average worker will be assembling walkie-talkies t hr after starting work. At what rate will the average worker be assembling walkie-talkies at 11 A.M.?
If two identical cans of soup placed on the scale have a combined weight of 31.15 oz, what are the largest and smallest possible weights of one of the cans?