Consider the following table of values:
Complete the data transformation by filling in the table of values for x^2.
Plot the y values against the x^{2} values.
Hence, draw the line that passes through these points.
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| x^2 | |||||
| y | 0 | 1 | 4 | 9 | 16 |
Consider the following points shown:
Complete the data transformation by filling in the table of values for the points shown on the graph:
| x^{2} | ||||
|---|---|---|---|---|
| y | -5 | -3 | 3 | 13 |
Plot the y values against the x^{2} values.
Hence, draw the line that passes through the points.
Consider the following table of values:
Complete the data transformation by filling in the table of values.
Does the transformation linearise the data?
| x | 1 | 3 | 7 | 9 |
|---|---|---|---|---|
| x^{2} | ||||
| y | 1 | 27 | 343 | 729 |
For each of the following graphs, draw the graph of y against x^{2}:
Consider the following points shown below:
Complete the data transformation by filling in the table of values for the points shown on the graph.
| \dfrac{1}{x} | ||||
|---|---|---|---|---|
| y | 10 | 5 | 2 | 1 |
Plot the y values against the \dfrac{1}{x} values.
Hence, draw the line that passes through these points.
Consider the following graph, and draw the graph of y against \dfrac{1}{x}.
Consider the following table of values:
Complete the data transformation by filling in the table of values.
Does the transformation linearise the data? Explain your answer.
| x | 1 | 2 | 4 | 5 |
|---|---|---|---|---|
| \dfrac{1}{x} | ||||
| y | 1 | 0.25 | 0.0625 | 0.04 |
Consider the following table of values:
Complete the data transformation by filling in the table of values.
Plot the y values against the \dfrac{1}{x} values.
Hence, draw the line that passes through the points.
| x | \dfrac{1}{6} | \dfrac{1}{4} | \dfrac{1}{2} | 1 |
|---|---|---|---|---|
| \dfrac{1}{x} | ||||
| y | -5 | -4 | -3 | - 2\dfrac{1}{2} |
Consider the following table of values, and draw the graph of y against \dfrac{1}{x}.
| x | \dfrac{1}{8} | \dfrac{1}{4} | \dfrac{1}{2} |
|---|---|---|---|
| y | 0 | - 1 | -\dfrac{3}{2} |
Consider the following table of values:
Complete the data transformation by filling in the table of values.
Plot the y values against the \log_{10} x values.
Hence, draw the line that passes through the points.
| x | 1 | 10 | 100 | 1000 |
|---|---|---|---|---|
| \log_{10} x | ||||
| y | 0 | 5 | 10 | 15 |
Consider the following points shown:
Complete the data transformation by filling in the table of values for the points shown on the graph.
| \log_{10} x | |||
|---|---|---|---|
| y | -3 | 7 | 17 |
Plot the y values against the \log_{10} x values.
Hence, draw the line that passes through the points.
Consider the following graph and draw the graph of y against \log_{10} x.
For the given table of values, draw the graph of y against \log_{10} x.
| x | 1 | 10 | 100 | 1000 |
|---|---|---|---|---|
| y | -8 | -11 | -14 | -17 |
For the following tables of values:
Complete the two different data transformations by filling in the table. Round your answers to three decimal places where necessary.
Using technology or otherwise, draw the graphs of the transformed data and state which transformation linearises the data.
| x | 1 | 2 | 4 | 6 |
|---|---|---|---|---|
| x^{2} | ||||
| \dfrac{1}{x} | ||||
| y | -\dfrac{31}{4} | -7 | -4 | -1 |
| x | 10 | 20 | 30 | 40 |
|---|---|---|---|---|
| x^{2} | ||||
| \log_{10} x | ||||
| y | -2 | -1.398 | -1.046 | -0.796 |
| x | 1 | 2 | 4 | 5 |
|---|---|---|---|---|
| \dfrac{1}{x} | ||||
| \log_{10} x | ||||
| y | -5.75 | -5.875 | -5.9375 | -5.95 |
A ball is dropped from rest at a certain height and the following data was recorded:
| t\text{ (time in seconds)} | 1 | 2 | 4 | 6 |
|---|---|---|---|---|
| d\text{ (distance travelled in metres)} | 4.9 | 19.6 | 78.4 | 176.4 |
Complete the following three data transformation by filling in the table of values:
Which transformation linearises the data?
| t^{2} | 4 | |||
|---|---|---|---|---|
| \dfrac{1}{t} | 0.17 | |||
| \log_{10} t | 0.30 | 0.60 | 0.78 | |
| d | 4.9 | 19.6 | 78.4 | 176.4 |
The concentration of hydrogen ions in a solution varies according to the concentration of hydroxide ions as shown in the following table:
| \text{Concentration of hydroxide (molarity)} | 10^{ - 3 } | 10^{ - 4 } | 10^{ - 5 } | 10^{ - 6 } | 10^{ - 7 } |
|---|---|---|---|---|---|
| \text{Concentration of hydrogen ions (molarity)} | 10^{ - 11 } | 10^{ - 10 } | 10^{ - 9 } | 10^{ - 8 } | 10^{ - 7 } |
Complete the following two data transformation by filling in the table of values:
| \text{Concentration of hydroxide}^{2} | 10^{ - 8 } | 10^{ - 10 } | 10^{ - 14 } | ||
|---|---|---|---|---|---|
| \dfrac{1}{\text{Concentration of hydroxide}} | 10^{3} | 10^{4} | 10^{7} | ||
| \text{Concentration of hydrogen ions} | 10^{ - 11 } | 10^{ - 10 } | 10^{ - 9 } | 10^{ - 8 } | 10^{ - 7 } |
Which transformation linearises the data?