Test
Function properties and transformations
This test develops understanding of even and odd functions and common graph transformations. Students identify shifts, reflections and scaling and construct a new function formula from a given transformation.
Time left: 00:00:00
Sample questions
- What type of parity has f(x) = x² + 4?
- Which formula describes a vertical shift of y = f(x) by ___ units?
- Which formula shifts y = f(x) by ___ units to the right?
- What transformation does y = −f(x) represent?
- How is y = f(x) changed vertically in y = ___f(x)?
Function properties and transformations
A function is described by its domain, range, zeros, sign, intervals of increase and decrease, extrema, parity and periodicity. These properties may be determined from a formula or graph.
Graph transformations
f(x) + a shifts vertically, f(x − a) shifts right and f(x + a) shifts left. The expressions −f(x) and f(−x) reflect the graph in the x-axis and y-axis respectively. A multiplier outside changes y-values, while a multiplier of the argument changes the horizontal scale.
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