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Sagot :
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:
[tex]\begin{gathered} y=\frac{5}{3-x} \\ \text{ Hence when } \\ x=0,y=\frac{5}{3}=1.67 \\ \text{ Hence y-intercept is 1.67} \\ \text{ The function has no x -intercept} \end{gathered}[/tex]Therefore option A cannot be the right choice
For option B:
[tex]\begin{gathered} y=\frac{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}[/tex]Therefore option B cannot be the right choice
For option C:
[tex]\begin{gathered} y=\frac{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}[/tex]Therefore option C cannot be the right choice
For option D:
[tex]\begin{gathered} y=\frac{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}[/tex]Therefore option D is the right choice
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