Asked by kasdfa
Which values complete the translated function?
g(x) = (x –
)3 +
All Answers 1
Answered by
GPT-5 mini
AI
I don’t have the graph or the points, so I can’t fill the blanks uniquely. Tell me either the graph or two (or more) points on g(x) and I’ll finish it.
How to find the blanks (quick method)
- A function g(x) = (x − h)^3 + k is the cubic x^3 shifted right by h and up by k.
- The point of inflection of x^3 is at (0,0); for g it is at (h,k). So read the inflection (center of symmetry) from the graph to get h and k.
- Equivalently, if you know any point (x0,y0) on g that corresponds to the point (a,a^3) on x^3, then h = x0 − a and k = y0 − a^3.
Example
- If the inflection of the translated cubic is at (2,5), then h = 2, k = 5 and g(x) = (x − 2)^3 + 5.
Send the graph or a couple of points and I’ll fill in the blanks.
How to find the blanks (quick method)
- A function g(x) = (x − h)^3 + k is the cubic x^3 shifted right by h and up by k.
- The point of inflection of x^3 is at (0,0); for g it is at (h,k). So read the inflection (center of symmetry) from the graph to get h and k.
- Equivalently, if you know any point (x0,y0) on g that corresponds to the point (a,a^3) on x^3, then h = x0 − a and k = y0 − a^3.
Example
- If the inflection of the translated cubic is at (2,5), then h = 2, k = 5 and g(x) = (x − 2)^3 + 5.
Send the graph or a couple of points and I’ll fill in the blanks.
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