Rate of Change of a Function Represented by a Table of Values

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The rate of change of a function represented by a table of values allows us to compare the variation of the values of X X (the independent variable of the function) with the variation of the values of Y Y (dependent variable of the function). This comparison enables us to determine if the intervals are fixed or not, and, consequently, if the rate of change is constant or not.

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Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

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For each X X we will fill in the corresponding Y Y .

We will see at what rate the Y Y variables increase in the table.
If the Y Y variables grow at the same rate, we can determine that the rate of change of the function is constant.

Function with Constant Rate of Change

We will illustrate this topic with the help of two different tables

Table of constant rate of change

Representation of the function in table

In this table, the first column represents the variables X X and the second, the variables Y Y according to their correspondence. 

If we look closely, we will see that there is a fixed rhythm that is maintained throughout all the values. For every increase in X X there is a corresponding increase of 1 1 in the Y Y variables.  

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Question 1

Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Question 2

Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Question 3

Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Function with a non-constant rate of change

Table representation of a function with a non-constant rate of change

Table representation of a function with a non-constant rate of change

Also in this table, the first column represents the X X variables and the second the Y Y variables according to their correspondence.

If we look closely, we will see that in this case there is no fixed rhythm that remains stable across all values.

If you are interested in this article, you might also be interested in the following articles:

Functions for Seventh Grade

Rate of Change of a Function

Rate of Change of a Function Represented Graphically

Constant Rate of Change

Variable Rate of Change

Rate of Change Represented with Steps in the Function's Graph

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Do you know what the answer is?
Question 1

Given the following graph, determine whether the rate of change is uniform or not

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

Question 2

Given the following graph, determine whether the rate of change is uniform or not

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–3–3–3–2–2–2–1–1–1111222333444555666000

Question 3

Given the following graph, determine whether function is constant

–9–9–9–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666000

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