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Sagot :
Answer:
- Reflected over the x-axis
- Compressed by a factor of 0.4.
- Translated 2 units left
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x}[/tex]
[tex]y' = -(0.4)\sqrt[3]{x-2}[/tex]
Required
The transformation from y to y'
First, y is reflected over the x-axis.
The transformation rule is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]y = \sqrt[3]{x}[/tex] becomes
[tex]y' = -\sqrt[3]{x}[/tex]
Next, it was compressed by a scale factor of 0.4
The rule is:
[tex]y' = k * y[/tex]
Where k is the scale factor (i.e. k = 0.4)
So, we have:
[tex]y' = 0.4 * -\sqrt[3]{x}[/tex]
[tex]y' = -(0.4)\sqrt[3]{x}[/tex]
Lastly, the function is translated 2 units left;
The rule is:
[tex](x,y) \to (x-2,y)[/tex]
So, we have:
[tex]y' = -(0.4)\sqrt[3]{x - 2}[/tex]
Answers:
-reflected over the x-axis
-translated 2 units right
-compressed by a factor of 0.4
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