Advanced Functions 12 | @ Wiz Kidz
Name : ________________________
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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