Answer:
Stretched by a factor of 2 and translated 8 units right and 5 units down
Step-by-step explanation:
Given
[tex]y =\sqrt[3]{8x-64}-5[/tex]
Taking greatest common factor.
[tex]y =\sqrt[3]{8 \times (x-8)}-5[/tex]
Separating the cube root over the multipliers
[tex]y =\sqrt[3]{8} \times \sqrt[3]{x-8}-5[/tex]
[tex]y = 2 \times \sqrt[3]{x-8}-5[/tex]
The parent cube root function is
[tex]y =\sqrt[3]{x}[/tex]
Stretched by a factor of 2 is equal to
[tex]y =2 \times \sqrt[3]{x}[/tex]
Then, translated 8 units right is equal to
[tex]y =2 \times \sqrt[3]{x - 8}[/tex]
Finally, translated 5 units down is equal to
[tex]y =2 \times \sqrt[3]{x - 8} - 5[/tex]
Transformation involves changing the position of a function.
The parent function is stretched vertically by a factor of 2, shifted right by 8 units, and shifted down by 5 units
The function is given as:
[tex]\mathbf{y=\sqrt[3]{8x-64}-5}[/tex]
A cube root function is represented as:
[tex]\mathbf{y=\sqrt[3]{x}}[/tex]
Multiply by 2
[tex]\mathbf{y=2 \times \sqrt[3]{x}}[/tex]
Express 2 as a cube root of 8
[tex]\mathbf{y=\sqrt[3]{8} \times \sqrt[3]{x}}[/tex]
Combine
[tex]\mathbf{y= \sqrt[3]{8x}}[/tex] ----- this means that the function is stretched vertically by 2
Subtract 8 from x
[tex]\mathbf{y= \sqrt[3]{8(x - 8)}}[/tex] ----- this means that the function is shifted right by 8 units
So, we have:
[tex]\mathbf{y= \sqrt[3]{8x - 64}}[/tex]
Lastly, subtract 5 from the function itself
[tex]\mathbf{y= \sqrt[3]{8x - 64} - 5}[/tex] ----- this means that the function is shifted down by 5 units
Read more about transformations at:
https://brainly.com/question/11707700
