What are the x- and y-intercepts of #y=sqrt(2x-1)#?

1 Answer
Jun 16, 2015

There is no intercept with the #y# axis.

The intercept with the #x# axis is at #(1/2, 0)#

Explanation:

If #y = sqrt(2x-1)# intercepted the #y# axis, then it would be where #x=0#, but then #y = sqrt(-1)# is not defined in #RR#.

In fact, #y = sqrt(2x-1)# is only defined for #x >= 1/2#.

If #y = 0# then #2x - 1 = 0# so #x = 1/2#. So the intercept with the #x# axis is at #(1/2, 0)#

graph{sqrt(2x-1) [-10, 10, -5, 5]}