Consider the following data set.
| x | 1 | 1.8 | 2.2 | 3 | 4 | 4.5 | 5.8 | 6.2 | 7 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 5 | 9.5 | 12.7 | 21 | 35 | 43.5 | 70.3 | 79.9 | 101 | 165 |
Use technology to create a scattergraph of this data.
Is the shape of the data appears to be logarithmic, reciprocal or parabolic?
Which transformation should we perform to linearise the data?
Square the x-values \left(x^2\right).
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Find the log of the x-values \left(\log x\right).
Complete the transformation of the x-values of the data and fill in this table.
| x^2 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| y | 5 | 9.5 | 12.7 | 21 | 35 | 43.5 | 70.3 | 79.9 | 101 | 165 |
Find the non-linear equation in the form y = k x^{2} + c.
Find the value for y when x = 70.
Consider the following data set.
| x | 1 | 0.9 | 1.5 | 2 | 3.5 | 4 | 5 | 6.2 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 6.5 | 6.4 | 7.1 | 8 | 12.1 | 14 | 18.5 | 25.2 | 46.5 | 56 |
Use technology to create a scattergraph of this data.
Is the shape of the data appears to be logarithmic, reciprocal or parabolic?
Which transformation should we perform to linearise the data?
Square the x-values \left(x^2\right).
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Find the log of the x-values \left(\log x\right).
Complete the transformation of the x-values of the data and fill in this table.
| x^2 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| y | 6.5 | 6.4 | 7.1 | 8 | 12.1 | 14 | 18.5 | 25.2 | 46.5 | 56 |
Find the non-linear equation in the form y = k x^{2} + c.
Find the value for y when x = 50.
Consider the following data set.
| x | \dfrac{1}{10} | 1 | 10 | 100 | 1000 |
|---|---|---|---|---|---|
| y | -12 | -2 | 8 | 18 | 28 |
Use technology to create a scattergraph of this data.
Is the shape of the data appears to be logarithmic, reciprocal or parabolic?
Which transformation should we perform to linearise the data?
Square the x-values \left(x^2\right).
Find the log of the x-values \left(\log x\right).
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Complete the transformation of the x-values of the data and fill in this table.
| \log x | |||||
|---|---|---|---|---|---|
| y | -12 | -2 | 8 | 18 | 28 |
Find the non-linear equation in the form y = k \log_{10} x + c.
Find the value for y when x = 7. Round your answer to two decimal places.
Consider the following data set.
| x | \dfrac{1}{10} | 1 | 10 | 100 | 1000 |
|---|---|---|---|---|---|
| y | 4.8 | 5 | 5.2 | 5.4 | 5.6 |
Use technology to create a scattergraph of this data.
Is the shape of the data appears to be logarithmic, reciprocal or parabolic?
Which transformation should we perform to linearise the data?
Square the x-values \left(x^2\right).
Find the log of the x-values \left(\log x\right).
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Complete the transformation of the x-values of the data and fill in this table.
| \log x | |||||
|---|---|---|---|---|---|
| y | 4.8 | 5 | 5.2 | 5.4 | 5.6 |
Find the non-linear equation in the form y = k \log_{10} x + c.
Find the value for y when x = 15. Round your answer to two decimal places.
Consider the following data set.
| x | \dfrac{1}{10} | \dfrac{1}{5} | \dfrac{4}{5} | 1 | 2 | 3 | 4 | 8 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| y | 24 | 9 | -\dfrac{9}{4} | -3 | -\dfrac{9}{2} | -5 | -\dfrac{21}{4} | -\dfrac{45}{8} | -\dfrac{57}{10} |
Use technology to create a scattergraph of this data.
Is the shape of the data appears to be logarithmic, reciprocal or parabolic?
Which transformation should we perform to linearise the data?
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Find the log of the x-values \left(\log x\right).
Square the x-values \left(x^2\right).
Complete the transformation of the x-values of the data and fill in this table.
| \dfrac{1}{x} | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| y | 24 | 9 | -\dfrac{9}{4} | -3 | -\dfrac{9}{2} | -5 | -\dfrac{21}{4} | -\dfrac{45}{8} | -\dfrac{57}{10} |
Find the non-linear equation in the form y = \dfrac{k}{x} + c.
Find the value for y when x = 100.
Consider the following data set.
| x | \dfrac{1}{10} | \dfrac{3}{10} | \dfrac{3}{5} | \dfrac{9}{10} | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|---|---|---|
| y | -\dfrac{1}{2} | -\dfrac{13}{6} | -\dfrac{31}{12} | -\dfrac{49}{18} | -\dfrac{11}{4} | -\dfrac{23}{8} | -\dfrac{35}{12} | -\dfrac{47}{16} | -\dfrac{59}{20} |
Use technology to create a scattergraph of this data.
Is the shape of the data appears to be logarithmic, reciprocal or parabolic?
Which transformation should we perform to linearise the data?
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Square the x-values \left(x^2\right).
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Complete the transformation of the x-values of the data and fill in this table.
| \dfrac{1}{x} | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| y | -\dfrac{1}{2} | -\dfrac{13}{6} | -\dfrac{31}{12} | -\dfrac{49}{18} | -\dfrac{11}{4} | -\dfrac{23}{8} | -\dfrac{35}{12} | -\dfrac{47}{16} | -\dfrac{59}{20} |
Find the non-linear equation in the form y = \dfrac{k}{x} + c.
Find the value for y when x = 10.
Consider the following data set.
| x | 1 | 2 | 2.8 | 4 | 5.5 | 8.5 | 10.8 | 15.2 | 20 | 39.4 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 4 | -5 | -16.52 | -41 | -83.75 | -209.75 | -342.92 | -686.12 | -1193 | -4650.08 |
Use technology to create a scattergraph of this data.
Is the shape of the data appears to be logarithmic, reciprocal or parabolic?
Which transformation should we perform to linearise the data?
Find the log of the x-values \left(\log x\right).
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Square the x-values \left(x^2\right).
Complete the transformation of the x-values of the data and fill in this table.
| x^2 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| y | 4 | -5 | -16.52 | -41 | -83.75 | -209.75 | -342.92 | -686.12 | -1193 | -4650.08 |
Find the non-linear equation in the form y = k x^{2} + c.
Find the value for y when x = 30.
Consider the following data set.
| x | 1 | 2 | 3 | 4 | 5 | 5.5 | 6.5 | 7.2 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 5.75 | 5 | 3.75 | 2 | -0.25 | -1.5625 | -4.5625 | -6.96 | -10 | -14.25 |
Use technology to create a scattergraph of this data.
Is the shape of the data appears to be logarithmic, reciprocal or parabolic?
Which transformation should we perform to linearise the data?
Find the reciprocal of the x-values \left(\dfrac 1x\right).
Square the x-values \left(x^2\right).
Find the log of the x-values \left(\log x\right).
Complete the transformation of the x-values of the data and fill in this table.
| x^2 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| y | 5.75 | 5 | 3.75 | 2 | -0.25 | -1.5625 | -4.5625 | -6.96 | -10 | -14.25 |
Find the non-linear equation in the form y = k x^{2} + c.
Find the value for y when x = 10.