4.04 Transform functions to straight lines
State the constant of proportionality of the following graphs:
State the equation of the following graphs:
In the form of y = k x^{2} + c
In the form of y = \dfrac{k}{x} + c
State the equation from the following table of values:
In the form of y = k x^{2} + c
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | -6 | -2 | 10 | 30 |
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | -7 | -4 | -1 | 2 |
In the form of y = \dfrac{k}{x} + c
| x | 1 | 2 | 3 | 6 |
|---|---|---|---|---|
| y | 7 | 4 | 3 | 2 |
| x | 1 | 2 | 4 | 6 |
|---|---|---|---|---|
| y | \dfrac{3}{2} | 2 | 3 | 4 |
Draw the graph of the following equations:
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 scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
What transformation should be performed to linearise the data?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 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 scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
What transformation should be performed to linearise the data?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 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 | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| y | 1 | 3 | 9 | 27 | 81 | 243 |
Use technology to create a scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
What transformation should be performed to linearise the data?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | ||||||
|---|---|---|---|---|---|---|
| y | 1 | 3 | 9 | 27 | 81 | 243 |
Find the non-linear equation in the form y = b^{x}.
Find the value for y when x = 7.
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 scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
What transformation should be performed to linearise the data?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| 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 |
|---|---|---|---|---|---|---|---|---|
| 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} |
Use technology to create a scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
What transformation should be performed to linearise the data?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | ||||||||
|---|---|---|---|---|---|---|---|---|
| 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} |
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 |
|---|---|---|---|---|---|---|---|---|---|
| y | 4 | -5 | -16.52 | -41 | -83.75 | -209.75 | -342.92 | -686.12 | -1193 |
Use technology to create a scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
What transformation should be performed to linearise the data?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| y | 4 | -5 | -16.52 | -41 | -83.75 | -209.75 | -342.92 | -686.12 | -1193 |
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 | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| y | 5 | 10 | 20 | 40 | 80 | 160 |
Use technology to create a scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | ||||||
|---|---|---|---|---|---|---|
| y | 5 | 10 | 20 | 40 | 80 | 160 |
Find the non-linear equation in the form y = A b^{x}.
Find the value for y when x = 10.
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 scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
What transformation should be performed to linearise the data?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 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.
Consider the following data set.
| x | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| y | \dfrac{4}{9} | \dfrac{4}{3} | 4 | 12 | 36 | 108 | 324 |
Use technology to create a scatter diagram of the data.
Does the shape of the data appear to be exponential, reciprocal or parabolic?
Complete the transformation of the x-values of the data and fill in a table of the form:
| ⬚ | |||||||
|---|---|---|---|---|---|---|---|
| y | \dfrac{4}{9} | \dfrac{4}{3} | 4 | 12 | 36 | 108 | 324 |
Find the non-linear equation in the form y = A b^{x}.
Find the value for y when x = 8.