which graph functions decrease over part of the domain and increase over the rest of the domain

Graphs of functions where there is a decrease over part of the domain and an increase over the rest can be represented by various types of functions. One of the most common examples is the graph of a quadratic function, which can be described by an equation of the form:

\[ f(x) = ax^2 + bx + c \]

When the coefficient \( a \) is positive, the graph opens upwards, and when \( a \) is negative, it opens downwards. In either case, there is a point on the graph called the vertex where the graph changes from increasing to decreasing (for \( a > 0 \)) or from decreasing to increasing (for \( a < 0 \)).

If \( a > 0 \), the graph decreases up to the vertex and then increases for the rest of the domain. If \( a < 0 \), it increases up to the vertex and then decreases.

Other examples include cubic functions, absolute value functions, and certain piecewise-defined functions. Each of these can show regions where they are increasing and regions where they are decreasing.