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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.

Question qty: 10
Duration in minutes: 14
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Sample questions

  • Which formula shifts y = f(x) by a units to the right?
  • Which formula describes a vertical shift of y = f(x) by a units?
  • What type of parity has f(x) = x² + 4?
  • What transformation does y = −f(x) represent?
  • How does a change inside f(x) differ from a change outside f?
  • How is y = f(x) changed vertically in y = af(x)?
  • The graph of y = a^x passes through (x, y). Find a.
  • Which function is odd?

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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