Function families and their parameters
Shift power and exponential functions with sliders, read domain, range and asymptote, find the inverse function as a reflection and match a graph with its term.
- France: grade 11
- Germany: grade 10
- Syria: grade 11
- Palestine: grade 9
- Ukraine: grade 9
Guide
For a power function y = a(x + b)c + d the term b in the bracket moves the graph to the LEFT by b, d moves it up. The vertex of y = (x + b)2 + d is at S(−b|d).
For an exponential function y = k·ax − b + c the line y = c is the asymptote, so the range is W = ]c;∞[ for k > 0. The graph passes through (b|k + c).
The inverse function is the reflection of the graph in the line y = x. The inverse function of y = ax is y = logax.
To find a term from a graph, first name the family (line, parabola, root, exponential, logarithm, sine), then read the shifts from the characteristic point.