Limits and Continuity — Quiz

Question 8 • Precalculus

Which function is continuous at x is equal to negative 4 ?

Answer

g of x equals inequality x squared minus 4 comma x is less than negative 4 inequality 5 x comma x is greater than or equal to negative 4

g of x is equal to the fraction with numerator open paren x plus 8 close paren times open paren x plus 4 close paren and denominator x plus 4

g of x equals inequality x squared comma x is less than negative 4 inequality negative 4 x comma x is greater than or equal to negative 4

g of x is equal to the fraction with numerator x and denominator open paren x plus 4 close paren squared

Explanation

For choice C, the left-hand limit at x = −4 is (−4)² = 16. The function’s value at −4 comes from the second rule, −4x, which gives −4(−4) = 16; since the limit and function value agree, the function is continuous there. The other choices either have a jump at −4 or are undefined there.

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