graph f(x)=|x-1|+1

Answer 1

Before you try to graph the function f, please graph these four simpler functions j, h, j and k:

First graph the function g(x) = x. It's a diagonal line (lower left to upper right) through the origin.

Then graph the function h(x) = x - 1. It looks just like the graph of g, except it's 1 unit lower. It's a diagonal line

(lower left to upper right) through the point (0, -1). Note that the graph of h also goes through the point (1, 0).

Then graph the function j(x) = |x - 1|. It looks just like the graph of h, except that the part below the x axis (i.e., below sea level) is reflected above the x axis (i.e., into the air). The graph of j is two diagonal lines radiating out from the point (1, 0), one line going to the upper left and one line going to the upper right.

Then graph the function f(x) = |x - 1| + 1. It looks just like the graph of j, except it's 1 unit higher. The graph of f is two diagonal lines radiating out from the point (1, 1), one line going to the upper left and one line going to the upper right.

Answer 2

f(x) = |x| graph is a V with the lines having slopes of -1 and 1, with the tip at the origin.

For f(x) = |x-1| +1, the V is shifted right one unit and up one unit.