standard_description: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
problem_activity: Task
Let $P = (0,1)$ and $Q = (1,2)$ in the $(x,y)$ plane.
Show that there is a unique linear function described by the equation $y = mx + b$ whose graph contains $P$ and $Q$: find $m$ and $b$.
Show that there is a unique exponential function described by the equation $y = ab^x$ whose graph contains $P$ and $Q$: find $a$ and $b$.
Show that there is more than one quadratic function described by the equation $y = ax^2 + bx
+c$ whose graph contains $P$ and $Q$.


aligns: no