Chapter Review
Chapter
Chapter 5
Section
Chapter Review
Purchase this Material for $10
You need to sign up or log in to purchase.
Subscribe for All Access
You need to sign up or log in to purchase.
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

Buy to View
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

Buy to View
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

Buy to View
Q1c

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

Buy to View
Q2a

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

Buy to View
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}

Buy to View
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}

Buy to View
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}

Buy to View
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}

Buy to View
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.

Buy to View
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}

Buy to View
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}

Buy to View
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}

Buy to View
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}

Buy to View
0.28mins
Q5d

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

Buy to View
Q6

Solve the equation algebraically.

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

Buy to View
Q7a

Solve the equation algebraically.

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

Buy to View
0.55mins
Q7b

Solve the equation algebraically.

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

Buy to View
Q7c

Solve the equation algebraically.

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

Buy to View
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?

Buy to View
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.

Buy to View
Q9

Solve for x.

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

Buy to View
2.58mins
Q10a

Solve for x.

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

Buy to View
1.24mins
Q10b

Solve for x.

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

Buy to View
Q10c

Solve for x.

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

Buy to View
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).

Buy to View
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.

Buy to View
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.

Buy to View
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.

Buy to View
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).

Buy to View
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.

Buy to View
Q15