y = \\frac{x + 2}{x + 9}\nwhat is the range of the function?\na. all real numbers except -2\nb. all real…

y = \\frac{x + 2}{x + 9}\nwhat is the range of the function?\na. all real numbers except -2\nb. all real numbers except -9\nc. all real numbers except 1\nd. all real numbers except -2 and -9\ne. all real numbers except -2, -9, and 1

y = \\frac{x + 2}{x + 9}\nwhat is the range of the function?\na. all real numbers except -2\nb. all real numbers except -9\nc. all real numbers except 1\nd. all real numbers except -2 and -9\ne. all real numbers except -2, -9, and 1

Answer

Explanation:

Step1: Rewrite the function

We rewrite $y = \frac{x + 2}{x+9}$ as $y=\frac{x + 9-7}{x + 9}=1-\frac{7}{x + 9}$.

Step2: Analyze the non - possible value of y

Since $\frac{7}{x + 9}\neq0$ for all real $x\neq - 9$, then $y=1-\frac{7}{x + 9}\neq1$. The domain of the original rational function is all real numbers except $x=-9$, but we are looking for the range. The value that $y$ cannot take is $y = 1$.

Answer:

C. all real numbers except 1