1. Summarize the Rational Function Task
Rational Functions
Summarize the Rational Function Task
Holt McDougal Algebra 2
Holt Algebra 2

2. Let’s make sure you got the conclusions form the task.
Given functions f(x) = (x – a)(x + b)(x – c) and g(x) = (x – d)(x + e) where a, b, c, d, and e are positive real numbers such that a ≠ b ≠ c ≠ d ≠ e,
Where are the roots of the function
d and -e

3. Given functions f(x) = (x – a)(x + b)(x – c) and g(x) = (x – d)(x + e) where a, b, c, d, and e are positive real numbers such that a ≠ b ≠ c ≠ d ≠ e, b) Where are the vertical asymptotes of the function
a, -b and c

4. Given functions f(x) = (x – a)(x + b)(x – c) and g(x) = (x – d)(x + e) where a, b, c, d, and e are positive real numbers such that a ≠ b ≠ c ≠ d ≠ e, c) Where are the roots of the function
d and -e

5. Given functions f(x) = (x – a)(x + b)(x – c) and g(x) = (x – d)(x + e) where a, b, c, d, and e are positive real numbers such that a ≠ b ≠ c ≠ d ≠ e, d) Where are the vertical asymptotes of the function
a, -b and c

6. d) Where are the vertical asymptotes of the function
Given functions f(x) = (x – a)(x + b)(x – c) and g(x) = (x – d)(x + e) where a, b, c, d, and e are positive real numbers such that a ≠ b ≠ c ≠ d ≠ e,
d) Where are the vertical asymptotes of the function
d and -e

7. What type of functions were f(x) and g(x)?
Polynomial Functions

8. 3. Give a definition of a rational function?
A rational function is a function whose rule can be written as a ratio of two polynomials.

9. For any simplified rational function, what information can you obtain from the numerator?
If you set the numerator = to 0, you determine the x-intercepts (zeros, solutions, roots).

10. 5. For any simplified rational function, what information can you obtain from the denominator?
If you set the denominator = to 0, you determine the vertical asymptotes.

11. Summarize one more time…..
Notice it says with no common factors!!
Factoring is ALWAYS the first step.

12. Example 3: Graphing Rational Functions with Vertical Asymptotes
Identify the zeros and vertical asymptotes of f(x) =
(x2 + 3x – 4)
x + 3
Step 1 Factor!! Then find the zeros & vertical
asymptotes.
Factor the numerator.
(x + 4)(x – 1)
x + 3
f(x) =
The numerator is 0 when x = –4 or x = 1.
Zeros: –4 and 1
The denominator is 0 when x = –3.
Vertical asymptote: x = –3

13. Vertical asymptote: x = –3
Example 3 Continued
Identify the zeros and vertical asymptotes of f(x) =
(x2 + 3x – 4)
x + 3
Vertical asymptote: x = –3
Step 2 Graph the function.
Plot the zeros and draw the asymptote. Then make a table of values to fill in missing points. x –8 –4
–3.5
–2.5 1 4 y
–7.2
4.5
–10.5
–1.3
3.4

14. Check It Out! Example 3
Identify the zeros and vertical asymptotes of f(x) =
(x2 + 7x + 6)
x + 3
Step 1 Facotr!! Find the zeros & vertical asymptotes.
(x + 6)(x + 1)
x + 3
f(x) =
Factor the numerator.
The numerator is 0 when x = –6 or x = –1 .
Zeros: –6 and –1
The denominator is 0 when x = –3.
Vertical asymptote: x = –3

15. Check It Out! Example 3 Continued
Identify the zeros and vertical asymptotes of f(x) =
(x2 + 7x + 6)
x + 3
Step 2 Graph the function.
Plot the zeros and draw the asymptote. Then make a table of values to fill in missing points.
Vertical asymptote: x = –3 x –7 –5 –2 –1 2 3 7 y
–1.5 –4
4.8 6
10.4

16. Cwk/Hwk
Worksheet 1-9