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
easyRepresent the function f(x) = 2x + 1 in four ways: equation, table of values, graph description, and verbal description.
Example 2
mediumA 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
easyConvert 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
hardA 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.