Practice Multiple Representations in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Every function can be expressed in four equivalent ways: as an algebraic formula, a table of input-output pairs, a graph on the coordinate plane, or a verbal description. Each representation highlights different properties and is useful in different contexts.

Same function, different views: y = 2x as formula, as table, as line, as 'doubling.'

Example 1

easy
Represent the function f(x) = 2x + 1 in four ways: equation, table of values, graph description, and verbal description.

Example 2

medium
A table gives values: x: 0,1,2,3 and f(x): 1,2,4,8. Identify the function type, write its equation, and describe its graph.

Example 3

easy
Convert the verbal description to an equation: 'The output is three less than twice the square of the input.' Then evaluate the function at x = 4.

Example 4

hard
A graph passes through (-2,0), (0,-4), and (1,0) and appears to be a parabola. Find the quadratic equation and verify using all three points.