Question

Which of the following describes the graph of y=\sqrt[3]{8x-64}-5 compared to the parent cube root function?

Answer 1

Answer:

Stretched by a factor of 2 and translated 8 units right and 5 units down

Step-by-step explanation:

Given  

$y =\sqrt[3]{8x-64}-5$

Taking greatest common factor.

$y =\sqrt[3]{8 \times (x-8)}-5$

Separating the cube root over the multipliers

$y =\sqrt[3]{8} \times \sqrt[3]{x-8}-5$

$y = 2 \times \sqrt[3]{x-8}-5$

The parent cube root function is

$y =\sqrt[3]{x}$

Stretched by a factor of 2 is equal to

$y =2 \times \sqrt[3]{x}$

Then, translated 8 units right is equal to

$y =2 \times \sqrt[3]{x - 8}$

Finally, translated 5 units down is equal to

$y =2 \times \sqrt[3]{x - 8} - 5$  

Answer 2

Answer: stretched by a factor of 2 and translated 8 units right and 5 units down

Explanation:

These is the set of choices that accompany with this question:


a) stretched by a factor of 2 and translated 64 units right and 5 units down
b) stretched by a factor of 8 and translated 8 units right and 5 units down
c) stretched by a factor of 2 and translated 8 units right and 5 units down
d) stretched by a factor of 8 and translated 64 units right and 5 units down


Solution:

Let's work a little the given function to compare it with the parent function.

1) The given function is y = ∛[8x - 64] - 5

2) Extract common factor 8 of the expression inside the square brackets:

y = ∛[ 8( x - 8) ] - 5

3) Extract 8 from the root:

y = 2∛(x - 8) - 5

4) The parent function is ∛x. Call the parent function g(x) => g(x) = ∛x

5) Compare: y is 2 * g(x - 8) - 5

6) Analyze the meaning of that:

g(x - 8) means that the graph of the function is translated 8 units to the right

scaling by 2 means that the graph is stretch vertically (by a scale factor of 2)

- 5 means that the entire graph is shifted 5 units downward.

So, the description of the graph y = ∛(8x - 64) - 5 compared to the parent cube root function is: stretched by a factor of 2 and translated 8 units right and 5 units down