91Ó°ÊÓ

Create a table of values for each function for values near its non-permissible value. Explain how your table shows whether a point of discontinuity or an asymptote occurs in each case. a) \(y=\frac{x^{2}-3 x}{x}\) b) \(y=\frac{x^{2}-3 x-10}{x-2}\) c) \(y=\frac{3 x^{2}+4 x-4}{x+4}\) d) \(y=\frac{5 x^{2}+4 x-1}{5 x-1}\)

Graph each function using technology and identify any asymptotes and intercepts. a) \(y=\frac{2 x+1}{x-4}\) b) \(y=\frac{3 x-2}{x+1}\) c) \(y=\frac{-4 x+3}{x+2}\) d) \(y=\frac{2-6 x}{x-5}\)

For each function, predict the locations of any vertical asymptotes, points of discontinuity, and intercepts. Then, graph the function to verify your predictions. a) \(y=\frac{x^{2}+4 x}{x^{2}+9 x+20}\) b) \(y=\frac{2 x^{2}-5 x-3}{x^{2}-1}\) c) \(y=\frac{x^{2}+2 x-8}{x^{2}-2 x-8}\) d) \(y=\frac{2 x^{2}+7 x-15}{9-4 x^{2}}\)

Write the equation of a possible rational function with each set of characteristics. a) vertical asymptotes at \(x=\pm 5\) and \(x\) -intercepts of -10 and 4 b) a vertical asymptote at \(x=-4,\) a point of discontinuity at \(\left(-\frac{11}{2}, 9\right)\) and an \(x\) -intercept of 8 c) a point of discontinuity at \(\left(-2, \frac{1}{5}\right)\) a vertical asymptote at \(x=3,\) and an \(x\) -intercept of -1 d) vertical asymptotes at \(x=3\) and \(x=\frac{6}{7},\) and \(x\) -intercepts of \(-\frac{1}{4}\) and 0

The intensity, \(I\), of light, in watts per square metre \(\left(\mathrm{W} / \mathrm{m}^{2}\right),\) at a distance, \(d,\) in metres, from the point source is given by the formula \(I=\frac{P}{4 \pi d^{2}},\) where \(P\) is the average power of the source, in watts. How far away from a 500 -W light source is intensity \(5 \mathrm{W} / \mathrm{m}^{2} ?\)

a) Predict the shape of the graph of \(y=\frac{2 x^{2}+2}{x^{2}-1}\) and explain your reasoning. b) Use graphing technology to confirm your prediction. c) How would the graph of each of the following functions compare to the one in part a)? Check using graphing technology. i) \(y=\frac{2 x^{2}-2}{x^{2}-1}\) ii) \(y=\frac{2 x^{2}+2}{x^{2}+1}\)

The time it takes for two people working together to complete a job is given by the formula \(T=\frac{a b}{a+b},\) where \(a\) and \(b\) are the times it takes for the two people to complete the same job individually. Sarah can set up the auditorium for an assembly in 30 min, but when she works with James they can set it up in 10 min. How long would it take James to set it up by himself?

In hockey, a player's shooting percentage is given by dividing the player's total goals scored by the player's total shots taken on goal. So far this season, Rachel has taken 28 shots on net but scored only 2 goals. She has set a target of achieving a \(30 \%\) shooting percentage this season. a) Write a function for Rachel's shooting percentage if \(x\) represents the number of shots she takes from now on and she scores on half of them. b) How many more shots will it take for her to bring her shooting percentage up to her target?

The coefficient, \(C,\) in parts per million per kelvin, of thermal expansion for copper at a temperature, \(T,\) in kelvins, can be modelled with the function \(C(T)=\frac{21.2 T^{2}-877 T+9150}{T^{2}+23.6 T+760}\). a) For what temperature is \(C(T)=15\) according to this model? b) By how many kelvins does the temperature have to increase for copper's coefficient of thermal expansion to increase from 10 to \(17 ?\)