How do you find the intercepts for y=(2x-1)/(3-x)?

Aug 25, 2016

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

Explanation:

When the function crosses the y-axis (y-intercept) then the corresponding x-coordinate will be zero. Substituting x = 0 into the function will give the value of the y-intercept.

$\Rightarrow y = \frac{0 - 1}{3 - 0} = - \frac{1}{3} \text{ is the y-intercept}$

Similarly, when the function crosses the x-axis (x-intercept) the corresponding y-coordinate will be zero. Substituting y = 0 into the function will give the value of the x-intercept.

$\Rightarrow 0 = \frac{2 x - 1}{3 - x}$

Now, the denominator of the function cannot be zero as this would make the function undefined. Hence the numerator must equal zero.

$\Rightarrow 2 x - 1 = 0 \Rightarrow x = \frac{1}{2} \text{ is the x-intercept}$
graph{(2x-1)/(3-x) [-10, 10, -5, 5]}