MATH 1024 PRECALCULUS Topic 3 Polynomial and Rational Functions

Prepared by Ms Janice WongSF 1

TOPIC 3: POLYNOMIAL AND RATIONAL FUNCTIONS

EXERCISES TO BE DONE IN THE CLASS ON JANUARY, 29.

1. Determine which of these functions are polynomial functions. For those that are, state

the degree. For those that are not, tell why not.

a) () = 52 + 44

b) () = ( 1)

c) () =25

3

2. Form a polynomial function whose real zeros and degree are given as below.

a) Zeros: -2, 2, 3; degree 3

b) Zeros: -3, 0, 4; degree 3

3. Homework (page 202, Q49; Ignore part d and part e, we sketch the curve)

*Please do the same thing for Q55 and Q59 (homework as stated in the notes)

() = 3( 7)( + 3)2 a) List the zeros and state its multiplicity.

b) Determine the intercepts if there is any.

c) Sketch the curve.

4. Find the domain of each rational function.

a) () =5

3+2

b) () =32+

327

5. Graph this rational function, () =2+12

24.

6. Solve these inequality.

a) 4 > 2 b) 152 > 33 c) (2 1)(2 )2( + 5) 0

d) +12

7

e) 5

3>

3

+1

f) (2+1)(2)

(1)(+1) 0

7. Find the inverse of the following one-one function. Sketch , 1 and = on the same axes.

a) () = 2 + 9, 0

b) () =4

+2