what is the range of $y = \\frac{2x + 1}{3x - 6}$?\na. all real numbers except $-\\frac{1}{2}$\nb. all real…

what is the range of $y = \\frac{2x + 1}{3x - 6}$?\na. all real numbers except $-\\frac{1}{2}$\nb. all real numbers except $-\\frac{1}{6}$\nc. all real numbers except 0\nd. all real numbers except $\\frac{2}{3}$\ne. all real numbers except 2

what is the range of $y = \\frac{2x + 1}{3x - 6}$?\na. all real numbers except $-\\frac{1}{2}$\nb. all real numbers except $-\\frac{1}{6}$\nc. all real numbers except 0\nd. all real numbers except $\\frac{2}{3}$\ne. all real numbers except 2

Answer

Explanation:

Step1: Let $y=\frac{2x + 1}{3x-6}$ and solve for $x$.

$y(3x - 6)=2x+1$ $3xy-6y=2x + 1$ $3xy-2x=1 + 6y$ $x(3y - 2)=1 + 6y$ $x=\frac{6y + 1}{3y-2}$

Step2: Find the value of $y$ for which $x$ is undefined.

The function $x=\frac{6y + 1}{3y-2}$ is undefined when the denominator $3y - 2=0$. Solving $3y-2 = 0$ gives $y=\frac{2}{3}$. So the range of $y=\frac{2x + 1}{3x-6}$ is all real - numbers except $\frac{2}{3}$.

Answer:

D. all real numbers except $\frac{2}{3}$