Precalculus, Chapter 5, 5.3, Section 5.3, Problem 46

You need to evaluate the x intercepts of the graph, hence, you need to remember that the graph intercepts x axis at y = 0. Hence, you need to solve for x the equation y= f(x) = 0 .
sin pi*x + cos pi*x = 0
You need to divide by cos pi*x , such that:
(sin pi*x)/(cos pi*x) + 1 = 0
tan pi*x = -1 => pi*x = arctan (-1) + k*pi
pi*x = -pi/4 + k*pi
Dividing by pi both sides, yields:
x = -1/4 + k
Hence, evaluating the x intercepts of the graph of the given function, yields x = k - 1/4 , where k in Z .