is the function given below continuous at x = 9? why or why not? f(x)=3x - 9 is f(x)=3x - 9 continuous at x…

is the function given below continuous at x = 9? why or why not? f(x)=3x - 9 is f(x)=3x - 9 continuous at x = 9? why or why not? a. no, f(x) is not continuous at x = 9 because lim f(x) is not equal to f(9). x→9 b. yes, f(x) is continuous at x = 9 because f(9) exists. c. yes, f(x) is continuous at x = 9 because lim f(x) is equal to f(9). x→9 d. no, f(x) is not continuous at x = 9 because lim f(x) and f(9) do not exist. x→9

is the function given below continuous at x = 9? why or why not? f(x)=3x - 9 is f(x)=3x - 9 continuous at x = 9? why or why not? a. no, f(x) is not continuous at x = 9 because lim f(x) is not equal to f(9). x→9 b. yes, f(x) is continuous at x = 9 because f(9) exists. c. yes, f(x) is continuous at x = 9 because lim f(x) is equal to f(9). x→9 d. no, f(x) is not continuous at x = 9 because lim f(x) and f(9) do not exist. x→9

Answer

Explanation:

Step1: Find f(9)

$f(9)=3\times9 - 9=18$

Step2: Find $\lim_{x\rightarrow9}f(x)$

$\lim_{x\rightarrow9}(3x - 9)=3\times9 - 9 = 18$

Step3: Check continuity condition

Since $\lim_{x\rightarrow9}f(x)=f(9) = 18$, the function is continuous.

Answer:

C. Yes, f(x) is continuous at x = 9 because $\lim_{x\rightarrow9}f(x)$ is equal to f(9).