Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 188: 126

Every polynomial function has a $y$-intercept. Some polynomial functions have no $x$-intercepts.

Every polynomial has function has a $y$-intercept which is: $y=f(0).$ Some polynomial functions don't have $x$ intercepts (when the image of the function doesn't touch nor cross the $x$-axis). The image is either just positive or just negative numbers (e.g.$f(x)=x^2+4$).