Question

Explain in your own words what the meaning of domain is. Also, explain why a denominator cannot be zero.

Find the domain for each rational expressions below.

Write the domain of each rational expression in set notation.

Do both of your rational expressions have excluded values in their domains? If yes, explain why they are to be excluded from the domains. If no, explain why no exclusions are necessary.

Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing. Do not write definitions for the words; use them appropriately in sentences describing your math work.

Domain

Excluded value

Set

Factor

Real numbers

16b2 – 1 2b2 + 11b – 6

c2 + 2c – 10 10c2 – 80c + 160

Answer 1

( 16b^2 - 1 ) / ( 2b^2 + 11b - 6 )

factoring the bottom

( 16b^2 -1 ) / ( b+6 ) ( 2b -1 )

excluded values of the function are found by setting denominator to 0

b + 6 = 0

b = -6

2b -1 = 0

b = 1/2

hence, excluded values are -6 , 1/2

since it will make the denominator 0 and if denominator is 0 rational function becomes undefined

domain is ( -infinity , -6 ) U ( -6 , 1/2 ) U ( 1/2 , infinity )

2) c^2 + 2c - 10 / ( 10c^2 - 80 c + 160 )

factoring the bottom 10 ( c - 4)^2

excluded values are c - 4 = 0

c = 4 since it will make denominator 0

domain is ( -infinity , 4 ) U ( 4 , infinity )