4.3 Warmups
We will be spending 2 days on Rational Functions. In class on Thurs, I will review Polynomial Functions and then go over 4.3 in class (Day 1 of 2 of Rational Functions). Please read through the textbook, watch videos, and go through the lecture notes -powerpoint is attached at the bottom.
Key terms: asymptotes, unbounded, improper, rational function
Objectives: find asymptotes in order to prepare for graphing, review polynomial long division
Answer the following True False questions.
1. T/F: The quotient of two polynomial expressions is a polynomial function.
2. T/F: To graph y = -x^2 you would reflect the graph of y = x^2 over the x axis.
3. T/F: The domain of every rational function is the set of all real numbers.
4. T/F: If an asymptote is neither horizontal nor vertical, it is called oblique.
5. T/F: If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients gives rise to the horizontal asymptote.
6. T/F: If the graph of a rational function R has the vertical asymptote x = 4, then x-4 must be in the denominator.
7. T/F: No graph of a rational function can have both a horizontal and an oblique asymptotes.
8. T/F: It is possible to have a graph of a rational function with both vertical and horizontal asymptotes.
9. T/F: The graphs of rational functions are smooth and continuous.
10. T/F: The domain of rational functions is the set of all real numbers.
Key terms: asymptotes, unbounded, improper, rational function
Objectives: find asymptotes in order to prepare for graphing, review polynomial long division
Answer the following True False questions.
1. T/F: The quotient of two polynomial expressions is a polynomial function.
2. T/F: To graph y = -x^2 you would reflect the graph of y = x^2 over the x axis.
3. T/F: The domain of every rational function is the set of all real numbers.
4. T/F: If an asymptote is neither horizontal nor vertical, it is called oblique.
5. T/F: If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients gives rise to the horizontal asymptote.
6. T/F: If the graph of a rational function R has the vertical asymptote x = 4, then x-4 must be in the denominator.
7. T/F: No graph of a rational function can have both a horizontal and an oblique asymptotes.
8. T/F: It is possible to have a graph of a rational function with both vertical and horizontal asymptotes.
9. T/F: The graphs of rational functions are smooth and continuous.
10. T/F: The domain of rational functions is the set of all real numbers.
I’ve decided to post the answers at the beginning of class in order to encourage you all to complete the Warmups.
It would help if you studied the section in advance so we can go through the harder problems in class rather than introducing the material. Here is the powerpoint. If you could go through it before class then I could do more board work.
PowerPoint here
Please prepare for class by going through the questions above, watching section videos from petesblog and looking over the powerpoint to get some notes.
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