# How do you find the intercepts for y=|x-1|?

Apr 7, 2017

X-intercept: $\left(1 , 0\right)$
Y-intercept: $\left(0 , 1\right)$

#### Explanation:

graph{(y-|x-1|)((x-1)^2+y^2-0.02)(x^2+(y-1)^2-0.02)=0 [-10, 10, -5, 5]}

The x-intercept is the point when the graph meets the x-axis. It is when $y = 0$. So, to find the x-intercept, set $y = 0$ and find the value of $x$: $0 = | x - 1 |$. The only value that satisfies this equation is $x = 1$. The x-intercept is $\left(1 , 0\right)$.

The y-intercept is the point when the graph meets the y-axis, or when $x = 0$. So, set $x = 0$ and find the value for $y$. Thus, $y = | x - 1 | = | 0 - 1 | = 1$. The y-intercept is $\left(0 , 1\right)$.

Be careful though, in some functions there can be multiple x-intercepts and y-intercepts.