This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the ...