Question

30 POINTSS!!

In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 4)3 + 6. The turning point of the graph is where the substance changes from a liquid to a gas. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function.

Answer 1

Answer:look below

Explanation:

1,f(x) = x^3

2:g(x) = f(x-4) which shifts f(x) 4 units to the right

3:g(x) = (x-4)^3

4:h(x) = g(x) + 6 shift g(x) 6 units up

5:h(x) = (x-4)^3 + 6

6;The turning point of f(x) is at (0,0), then shift 4 units to the right and 6 units up, I got (4,6)

Answer 2

f(x) = x^3 ... parent cubic function
g(x) = f(x-4) ... shifting f(x) 4 units to the right
g(x) = (x-4)^3
h(x) = g(x) + 6 ... shifting g(x) 6 units up
h(x) = (x-4)^3 + 6

The turning point of f(x) is at (0,0)
Applying the shifting of 4 units to the right and 6 units up, we get to (4,6) as the new turning point for h(x). This also the turning point for T(x) as well.

What does it mean? Well that part isn't clear to me because its not clear what x and T(x) represent. I'm assuming T(x) is temperature though I don't know what x represents. It's possible that x represents time though again I'm not sure about this part.