Multiple Representations Math Example 3

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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

Solution

1
Translate: 'twice the square of the input' $= 2x^2$ ; 'three less than' $\Rightarrow$ subtract $3$ . So $f(x) = 2x^2 - 3$ .
2
Evaluate: $f(4) = 2(16)-3 = 32-3 = 29$ .

Answer

f(x) = 2x^2 - 3

;

f(4) = 29

Translating verbal descriptions to algebraic equations requires careful attention to order of operations. 'Three less than twice the square' means compute

2x^2

first, then subtract

3

About Multiple Representations

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.

Learn more about Multiple Representations →

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Example 2 medium

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Example 4 hard

A graph passes through [formula], [formula], and [formula] and appears to be a parabola. Find the qu

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Related Concepts

Function Coordinate Plane