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CLEP Precalculus study materials
CLEP Precalculus study resources

CLEP Precalculus: Representations of Functions: Symbolic, Graphical, and Tabular

CLEP Precalculus · Work through your exam, one topic at a time.

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Representations of Functions: Symbolic, Graphical, and Tabular

The Representations of Functions: Symbolic, Graphical, and Tabular domain tests translation between the three views. A question may give a formula and ask for a graph feature, a table and ask for a rate, or a graph and ask for a model. What is being measured is your ability to extract the same information expressed in a different language.

What to read off each representation

  • Symbolic to graph: zeros, y-intercept, vertical asymptotes where the denominator vanishes, holes where a factor cancels, horizontal asymptotes from comparing degrees, and end behavior.
  • Table to rate: the average rate of change between two rows is the slope of the secant line, (y2 - y1)/(x2 - x1).
  • Table to model: constant first differences mean linear growth; constant ratios of successive outputs mean exponential growth y = a · b^x.
  • Graph to symbol: intercepts, intervals of increase and decrease, local extrema, symmetry, domain and range restrictions, and piecewise breakpoints signaled by open or closed dots.
  • Piecewise functions are evaluated by selecting the branch whose condition contains the input; a closed dot includes the endpoint, an open dot excludes it.

Worked example

A table lists g(0) = 6, g(1) = 18, g(2) = 54, g(3) = 162. First differences are 12, 36, 108, which are not constant, so the pattern is not linear. Ratios of successive outputs are 18/6 = 3, 54/18 = 3, and 162/54 = 3, which are constant, so the function is exponential with base 3. The output at x = 0 is the initial value, so g(x) = 6 · 3^x. Substituting x = 2 gives 6 · 9 = 54, matching the table row.

Traps that cost marks

  • Reporting the average rate of change as a y-value instead of a quotient of differences.
  • Declaring a table linear from two points; two points fit infinitely many functions.
  • Confusing a vertical asymptote with a zero, or a removable hole with an asymptote.
  • Misreading the axis scale - one gridline may represent 2 or 5 units, not 1.
  • Using the wrong piecewise branch exactly at a boundary value.