Vertical Dilations
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Question 1 of 5
1. Question
Dilate (stretch/shrink) `y=lnx` vertically by a factor of `1/3`.
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A dilation is to stretch or to shrink the shape of a curve.Vertical dilations (stretch/shrink) are shown by `y=color(red)(k)f(x)` where `k` is the vertical dilation factor.If `0<color(red)(k)<1`, then the graph is compressed.If `color(red)(k)>1`, then the graph is stretched.To dilate (stretch/shrink) `y=lnx` vertically by a factor of `color(red)(1/3)`, use `y=color(red)(k)f(x)` where `color(red)(k)` is the vertical dilation factor. This means that `color(red)(k=1/3)`.The equation for the new dilated equation is `y=color(red)(1/3)lnx`.Since `color(red)(k=1/3)` then the graph is compressed vertically as it will be further away from the y-axis.Use a table of values to find the `y` values for both the original and dilated graphs.`x` `1/2` `1` `3` `lnx` `-0.7` `0` `1.1` `1/3lnx` `-0.2` `0` `0.37` Sketch the graph of `y=lnx` and `y=1/3lnx` using the table of values.
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Question 2 of 5
2. Question
Dilate (stretch/shrink) `y=x^2` vertically by a factor of `3`.
Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.Vertical dilations (stretch/shrink) are shown by `y=color(red)(k)f(x)` where `k` is the vertical dilation factor.If `0<color(red)(k)<1`, then the graph is shrinked.If `color(red)(k)>1`, then the graph is stretched.To dilate (stretch/shrink) `y=x^2` vertically by a factor of `color(red)(3)`, use `y=color(red)(k)f(x)` where `color(red)(k)` is the vertical dilation factor. This means that `color(red)(k=3)`.`y=color(red)(3)x^2, color(red)(k=3)`, therefore the graph is stretched vertically along the y-axis and it will appear narrower.Use a table of values to find the `y` values for both the original and dilated graphs.`x` `-2` `-1` `0` `1` `2` `x^2` `4` `1` `0` `1` `4` `3x^2` `12` `3` `0` `3` `12` Sketch the graph of `y=x^2` and `y=3x^2` using the table of values.
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Question 3 of 5
3. Question
Dilate (stretch/shrink) `y=e^x` vertically by a factor of `1/4`.
Correct
Great Work!
Incorrect
A dilation is to stretch or to shrink the shape of a curve.Vertical dilations (stretch/shrink) are shown by `y=color(red)(k)f(x)` where `k` is the vertical dilation factor.If `0<color(red)(k)<1`, then the graph is compressed.If `color(red)(k)>1`, then the graph is stretched.To dilate (stretch/shrink) `y=e^x` vertically by a factor of `color(red)(1/4)`, use `y=color(red)(k)f(x)` where `color(red)(k)` is the vertical dilation factor. This means that `color(red)(k=1/4)`.The equation for the new dilated equation is `y=color(red)(1/4)e^x`.Since `color(red)(k=1/4)` the graph is compressed vertically. It is further away from the y-axis.Use a table of values to find the `y` values for both the original and dilated graphs.`x` `0` `1` `2` `3` `e^x` `1` `2.7` `7.4` `20` `1/4e^x` `1/4` `0.7` `1.9` `5` Sketch the graph of `y=e^x` and `y=1/4e^x` using the table of values.
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Question 4 of 5
4. Question
Dilate (stretch/shrink) `y=x^2` vertically by a factor of `1/2`.
Correct
Great Work!
Incorrect
A dilation is to stretch or to shrink the shape of a curve.Vertical dilations (stretch/shrink) are shown by `y=color(red)(k)f(x)` where `k` is the vertical dilation factor.If `0<color(red)(k)<1`, then the graph is compressed.If `color(red)(k)>1`, then the graph is stretched.To dilate (stretch/shrink) `y=x^2` vertically by a factor of `color(red)(1/2)`, use `y=color(red)(k)f(x)` where `color(red)(k)` is the vertical dilation factor. This means that `color(red)(k=1/2)`.The equation for the new dilated equation is `y=color(red)(1/2)x^2`.Since `color(red)(k=1/2)` the graph is compressed vertically so it is further away from the y-axis.Use a table of values to find the `y` values for both the original and dilated graphs.`x` `1` `2` `3` `4` `x^2` `1` `4` `9` `16` `1/2x^2` `1/2` `2` `9/2` `8` Sketch the graph of `y=x^2` and `y=1/2x^2` using the table of values.
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Question 5 of 5
5. Question
Dilate (stretch/shrink) `y=|x|` vertically by a factor of `4`.
Correct
Great Work!
Incorrect
A dilation is to stretch or to shrink the shape of a curve.Vertical dilations (stretch/shrink) are shown by `y=color(red)(k)f(x)` where `k` is the vertical dilation factor.If `0<color(red)(k)<1`, then the graph is compressed.If `color(red)(k)>1`, then the graph is stretched.To dilate (stretch/shrink) `y=|x|` vertically by a factor of `color(red)(4)`, use `y=color(red)(k)f(x)` where `color(red)(k)` is the vertical dilation factor. This means that `color(red)(k=4)`.The equation for the new dilated equation is `y=color(red)(4)|x|`.Since `k=4` this graph will be stretched vertically meaning it will come closer to the y-axisUse a table of values to find the `y` values for both the original and dilated graphs.`x` `1` `2` `3` `4` `|x|` `1` `2` `3` `4` `4|x|` `4` `8` `12` `16` Sketch the graph of `y=|x|` and `y=4|x|` using the table of values.
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