Question 1·Easy·Two-Variable Data: Models and Scatterplots
The table shows selected values from a function .
Which of the following is the best description of the function ?
For questions that ask you to describe a function from a table, first decide if the function is increasing or decreasing by scanning whether the y-values go up or down as x increases. Next, distinguish linear from exponential by checking for a constant difference (linear) versus a constant ratio (exponential) between consecutive y-values. Doing quick mental subtraction and, if needed, rough division lets you classify the function type quickly without any formal equation.
Hints
Look at how the outputs change
Compare the values in the table as increases by 1. Are the outputs getting larger or smaller?
Check the amount of change
Find the difference between each pair of consecutive values. Is this difference the same each time?
Linear vs. exponential pattern
Ask yourself: Do the values change by adding the same number each time, or by multiplying by about the same number each time?
Desmos Guide
Enter the table into Desmos
Create a table in Desmos with the values in the first column and the corresponding values in the second column. Look at the plotted points on the graph.
Observe the pattern of the points
Notice whether the points go up or down as you move left to right (increasing vs. decreasing), and whether they appear to lie on a straight line or curve. Also, check if the change in between points is a constant amount or if the values are being multiplied by about the same factor each time; use this to decide which answer choice best matches.
Step-by-step Explanation
Compare consecutive function values
Look at how changes as increases by 1.
Compute the differences between consecutive values:
Each time increases by 1, increases by 1.
Decide whether the function is increasing or decreasing
From the table, the values go as goes from to .
Since the numbers are getting larger as increases, the function is increasing, not decreasing.
Decide whether the pattern is linear or exponential
To tell linear from exponential:
- A linear pattern has a constant difference between consecutive values.
- An exponential pattern has a constant ratio between consecutive values.
Here, the differences are all , so the difference is constant.
Check the ratios:
These ratios are not the same, so the function is not exponential.
Match your observations to the answer choices
We found that:
- The function’s values are going up as increases (so it is increasing).
- The function changes by a constant amount (so it is linear, not exponential).
Therefore, the best description of is Increasing linear.