Question

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

Answer 1

x-intercept= `1/2`
y-intercept =`-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.

`rArry=(0-1)/(3-0)=-1/3" 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.

`rArr0=(2x-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.

`rArr2x-1=0rArrx=1/2" is the x-intercept"`
graph{(2x-1)/(3-x) [-10, 10, -5, 5]}