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Question 2 • Algebra II

Which function has a domain where x is not equal to 3 and a range where y is not equal to 2 ?

Answer
A
f of x is equal to the fraction with numerator 2 times open paren x plus 5 close paren and denominator open paren x plus 3 close paren
B
f of x is equal to the fraction with numerator open paren x plus 5 close paren and denominator open paren x minus 3 close paren
C
f of x is equal to the fraction with numerator open paren x minus 5 close paren and denominator x plus 3
D
f of x is equal to the fraction with numerator 2 times open paren x plus 5 close paren and denominator open paren x minus 3 close paren

Explanation

Choice A has denominator x − 3, so its domain excludes x = 3. To check the range, set 2(x + 5)/(x − 3) equal to 2; this gives 2x + 10 = 2x − 6, which is impossible. Therefore y can never equal 2, so the range excludes 2 as required.

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