Question

-1 08-62 72 4 6 8 ist in i isi 4 5 O A. 3- x V 2 + 3x 2-X B. .3+x 2-X O O C. v= 3 + 2x 2- x 3+3 O O D.

Answer 1

The function in the graph has a y-intercept that is approximately 1.5

and

an x-intercept that is approximately -1.8.

We will now check which of the functions in the options has x- and y-intercepts that are close to that of the function in the graph.

For option A:

`\begin{gathered} y=(5)/(3-x) \\ \text{ Hence when } \\ x=0,y=(5)/(3)=1.67 \\ \text{ Hence y-intercept is 1.67} \\ \text{ The function has no x -intercept} \end{gathered}`

Therefore option A cannot be the right choice

For option B:

`\begin{gathered} y=(2+3x)/(2-x) \\ \text{ Hence when } \\ x=0,y=1 \\ \text{ Hence y-intercept is 1 and it is not close to 1.67} \end{gathered}`

Therefore option B cannot be the right choice

For option C:

`\begin{gathered} y=(3+x)/(2-x) \\ \text{ Hence when } \\ x=0,y=1.5 \\ \text{ Hence y-intercept is 1.5 and it is close to 1.67} \\ \text{ When y = 0} \\ x=-3 \\ \text{ Hence, x-intercept is -3 and it is not close to }-1.8 \end{gathered}`

Therefore option C cannot be the right choice

For option D:

`\begin{gathered} y=(3+2x)/(2-x) \\ \text{ Hence when } \\ x=0,y=1.5 \\ \text{ Hence y-intercept is 1.5 and it is close to 1.67} \\ \text{ When y = 0} \\ x=-1.5 \\ \text{ Hence, x-intercept is -1.5 and it is close to }-1.8 \end{gathered}`

Therefore option D is the right choice