For the following exercises, determine whether the table...

Name: Problem 23, Chapter 4: Precalculus
Uploaded: 2020-11-17T06:36:47-08:00
Duration: 3 min 6 s
Channel: Oluwadamilola Ameobi
Description: For the following exercises, determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.

For the following exercises, determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.

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Key Concepts

Exponential Functions

An exponential function can be expressed in the form y = ab^x, where a and b are constants and b is a positive real number not equal to 1. The defining characteristic of exponential functions is that they have a constant ratio between consecutive outputs, meaning that dividing one output by its preceding output yields the same number. This constant multiplicative factor is what distinguishes exponential growth or decay.

Data Analysis Using Tables

When a table of values is provided, one can determine the type of function represented by examining the pattern in the y-values. For a linear function, the differences between consecutive y-values are constant. For an exponential function, the ratio of successive y-values remains constant. Detecting these patterns in tabulated data helps in classifying the function and, if applicable, finding the parameters that define either a linear or an exponential equation.

Linear Functions

A linear function is one that can be written in the form y = mx + b, where m and b are constants. The key characteristic of a linear function is that it exhibits a constant rate of change, which means the difference between successive y-values is the same throughout the domain. This constant difference is known as the slope, and it indicates that the graph of the function is a straight line.

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