Question

Identify a possible graph for function $f$ given by
$f\left(x\right)=\frac{(2x-3)}{(x-1)}$

• A. graph a
• B. graph b
• C. graph c
• D. graph d

Answer 1

The correct option is D graph d

Let $y=-\frac{2x-3}{x-1}$

The graph of $f\left(x\right)$ in this example is the graph of $y=-\frac{2x-3}{x-1}$. It is easy to generate points on the graph.

Choose a value for the first coordinate, then evaluate $y$ at that number to find the second coordinate.

The several values for $x$ and the function $y$ evaluated at those numbers.

If $x=0$, then $y=-\frac{2\left(0\right)-3}{0-1}=3$implies the point is $(0,3)$.

If $x=2$, then $y=-\frac{2\left(2\right)-3}{2-1}=1$implies the point is $(2,1)$.

If $x=3$, then $y=-\frac{2\left(3\right)-3}{3-1}=\frac{3}{2}$implies the point is $(3,\frac{3}{2})$.

Hence, the graph of the function is shown above.