Advanced Functions 12 | @ Wiz Kidz



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MHF4U1

Unit 3: Rational Functions

|K/U |APP |COM |TH |

|/17 |/7 |/10 |/17 |

|KNOWLEDGE/UNDERSTANDING |

1. Find the horizontal/slant asymptotes for the following rational functions: [3K]

a) f(x) [pic] [pic]

b) f(x) [pic] [pic]

c) [pic]

2. Identify any holes in the graph of f(x)[pic][pic]. Graph the function. [3K]

[pic]

3. Solve the following equality. Show a geometric representation of your solution. [3K]

(a) [pic]

4. Solve the following inequality. Show a geometric representation of your solution.

a) [pic] [4K]

5. Graph the function: [pic] [4K]

[pic]

|APPLICATION |

1. Salt water flows into a large tank of pure water. The concentration of the salt in the tank at t minutes is given by [pic], were c is measured in grams/liter. Properly label the axes.

a. When does the concentration in the tank reach 5 grams/liter?

b. When is the concentration of salt in the large tank less than 3 grams/litre? [7T]

|COMMUNICATION |

1. Which graph represents[pic]? Explain your reasoning. [2C]

A B

C D

Reasons:

2. What is the geometric meaning of the equality 4/(X-2) = 3 ? Sketch the graph to show where the solution would be. [2C]

3. What is the geometric meaning of the rational inequality 1/(x+1)(x-2) < 0 ? Sketch the graph and show where the solution(s) would be. [2C]

4. Explain why the inequality [pic] has no solution [2C]

5. If [pic]is a polynomial function, does [pic] always have to have a horizontal asymptote? If no, provide a counterexample. [2C]

|THINKING |

1. Write an equation for the following scenarios: [4T]

a) A rational quadratic function with no Vas

b) A rational quadratic function with one VA

c) A rational quadratic function with two VAs

d) A rational quadratic function with a slant asymptote

2. Determine a possible equation for each function: [4T]

A. B.

3. Write an equation for a rational function whose graph of the form [pic] has all the indicated features. [4T]

• X-intercept of [pic]

• Y-intercept of [pic]

• VA with equation [pic]

• HA with equation [pic]

4. Analyze and sketch the rational function: [pic] [5T]

BONUS +2

Determine the equation of a rational function with vertical asymptote [pic], a hole at [pic]and a horizontal asymptote [pic]

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