Chapter Review
Chapter
Chapter 5
Section
Chapter Review
Solutions 31 Videos

For the function, determine the domain and range, intercepts, positive/negative intervals, and increasing and decreasing intervals. Use this information to sketch a graph of the reciprocal function.

f(x) = 3x + 2

Q1a

For the function, determine the domain and range, intercepts, positive/negative intervals, and increasing and decreasing intervals. Use this information to sketch a graph of the reciprocal function.

\displaystyle f(x) = 2x^2 + 7x -4 

Q1b

For the function, determine the domain and range, intercepts, positive/negative intervals, and increasing and decreasing intervals. Use this information to sketch a graph of the reciprocal function.

\displaystyle f(x) =2x^2 + 2 

Q1c

Given the graphs of f(x) below, sketch the graphs of \displaystyle \frac{1}{f(x)} 

Q2a

Given the graph of f(x) below, sketch the graphs of y = \frac{1}{f(x)}

Q2b

For the function, determine the equations of any vertical asymptotes, the locations of any holes, and the existence of any horizontal or oblique asymptotes.

\displaystyle y = \frac{1}{x+ 17} 

Q3a

For the function, determine the equations of any vertical asymptotes, the locations of any holes, and the existence of any horizontal or oblique asymptotes.

\displaystyle y = \frac{2x}{5x+ 3} 

Q3b

For the function, determine the equations of any vertical asymptotes, the locations of any holes, and the existence of any horizontal or oblique asymptotes.

\displaystyle y = \frac{3x+ 33}{-4x^2 -42x + 22} 

Q3c

For the function, determine the equations of any vertical asymptotes, the locations of any holes, and the existence of any horizontal or oblique asymptotes.

\displaystyle y = \frac{3x^2 -2}{x -1} 

Q3d

The population of locusts in a Prairie a town over the last 50 years is modelled by the function \displaystyle f(x) = \frac{75x}{x^2 + 3x +2} . The locust population is given in hundreds of thousands. Describe the locust population in the town over time, where x is time in years.

Q4

For the function, determine the domain, intercepts, asymptotes, and positive/negative intervals. Use these characteristics to sketch the graph of the function. Then describe where the function is increasing or decreasing.

\displaystyle f(x) = \frac{2}{x + 5} 

Q5a

For the function, determine the domain, intercepts, asymptotes, and positive/negative intervals. Use these characteristics to sketch the graph of the function. Then describe where the function is increasing or decreasing.

\displaystyle f(x) = \frac{4x -8}{x -2} 

0.46mins
Q5b

For the function, determine the domain, intercepts, asymptotes, and positive/negative intervals. Use these characteristics to sketch the graph of the function. Then describe where the function is increasing or decreasing.

\displaystyle f(x) =\frac{x -6}{3x - 18} 

0.37mins
Q5c

For the function, determine the domain, intercepts, asymptotes, and positive/negative intervals. Use these characteristics to sketch the graph of the function. Then describe where the function is increasing or decreasing.

\displaystyle f(x) = \frac{4x}{2x + 1} 

0.28mins
Q5d

Describe how you can determine the behaviour of the values of a rational function on either side of a vertical asymptote.

Q6

Solve the equation algebraically.

\displaystyle \frac{x-6}{x+ 2} = 0 

Q7a

Solve the equation algebraically.

\displaystyle 15x + 7 = \frac{2}{x} 

0.55mins
Q7b

Solve the equation algebraically.

\displaystyle \frac{2x}{x- 12} = \frac{-2}{x+ 3} 

Q7c

Solve the equation algebraically.

\displaystyle \frac{x + 3}{-4x} = \frac{x- 1}{-4} 

0.32mins
Q7d

A group of students have volunteered for the student council car wash. Janet can wash a car in m minutes. Rodriguez can wash a car in m- 5 minutes, while Nick needs the same amount of time as Janet. If they all work together, they can wash a car in about 3.23 minutes. How long does Janet take to wash a car?

Q8

The concentration of a toxic chemical in a spring-fed lake is given by the equation \displaystyle c(x) = \frac{50x}{x^2 +3x + 6} , where c is given in grams per litre and x is the time in days. Determine when the concentration of the chemical is 6.16 g/L.

Q9

Solve for x.

 \displaystyle -x + 5 < \frac{1}{x + 3} 

2.58mins
Q10a

Solve for x.

 \displaystyle \frac{55}{3x+ 4} > -x 

1.24mins
Q10b

Solve for x.

 \displaystyle \frac{2x}{3x +4} > \frac{x}{x + 1} 

Q10c

Solve for x.

 \displaystyle \frac{x}{6x -9} \leq \frac{1}{x} 

Q10d

A biologist predicted that the population of tadpoles in a pond could be modelled by the function \displaystyle f(t) = \frac{40t}{t^2 + 1} , where t is given in days. The function that actually models the tadpole population is \displaystyle g(t) = \frac{45t}{t^2 + 8t + 7} . Determine where g(t) > f(t).

Q11

Estimate the slope of the line that is tangent to each function at the given point. At what point(s) is it not possible to draw a tangent line?

\displaystyle f(x) = \frac{x+ 3}{x-3}  where x = 4.

Q12a

Estimate the slope of the line that is tangent to each function at the given point. At what point(s) is it not possible to draw a tangent line?

\displaystyle f(x) = \frac{2x -1}{x^2 +3x + 2}  where x = 1.

Q12b

The concentration, c, of a drug in the bloodstream t hours after the drug was taken orally is given by \displaystyle c(t) = \frac{5t}{t^2 +7} , where c is measured in milligrams per litre.

a) Calculate the average rate of change in the drug's concentration during the first 2 h since ingestion.

b) Estimate the rate at which the concentration of the drug is changing after exactly 3h.

c) Graph c(t) on a graphing calculator. When is the concentration of the drug increasing the fastest in the bloodstream? Explain.

Q13

Given the function  \displaystyle f(x) = \frac{2x}{x -4} , determine the coordinates of a point on f(x) where the slope of the tangent line equals the slope of the secant line that passes through A(5, 10) and B(8, 4).

Q14

Describe what happens to the slope of a tangent line on the graph of a rational function as the x-coordinate of the point of tangency

a) gets closer and closer to the vertical asymptote.

b) grows larger in both the positive and negative direction.