Multiple Representations Math Example 2

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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.

Solution

1
Look for a pattern: $1, 2, 4, 8$ — each value doubles. This is exponential growth with ratio $2$ .
2
Equation: $f(x) = 1 \cdot 2^x = 2^x$ (since $f(0)=1=2^0$ ).
3
Graph description: starts at $(0,1)$ , increases steeply, never touches the $x$ -axis; horizontal asymptote at $y=0$ for $x \to -\infty$ .

Answer

f(x) = 2^x

; exponential function, increasing, asymptote

y=0

When consecutive ratios in a table are constant, the function is exponential. Recognizing this pattern from a table and translating it to an equation demonstrates fluency in switching between representations.

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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Represent the function [formula] in four ways: equation, table of values, graph description, and ver

Example 3 easy

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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