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Fill in the equation for this function:

[tex]\[ y = [?](x - \square)^3 + \square \][/tex]


Sagot :

To fill in the equation for this function, let's first identify and define our parameters based on the given answer:

- [tex]\( a = 1 \)[/tex]
- [tex]\( h = 0 \)[/tex]
- [tex]\( k = 0 \)[/tex]

The general form of a cubic function we are considering is:
[tex]\[ y = a(x - h)^3 + k \][/tex]

Plugging in the values we have:

1. Replace [tex]\( a \)[/tex] with 1:
[tex]\[ y = 1(x - h)^3 + k \][/tex]

2. Replace [tex]\( h \)[/tex] with 0:
[tex]\[ y = 1(x - 0)^3 + k \][/tex]
This simplifies to:
[tex]\[ y = x^3 + k \][/tex]

3. Finally, replace [tex]\( k \)[/tex] with 0:
[tex]\[ y = x^3 + 0 \][/tex]

The equation for the function then simplifies further to just:
[tex]\[ y = x^3 \][/tex]

So, the completed equation is:
[tex]\[ y = 1(x - 0)^3 + 0 \][/tex]

In the original template:
[tex]\[ y = [1](x - \underbrace{0}_{\square})^3 + \underbrace{0}_{\square} \][/tex]

Thus, the completed function is:
[tex]\[ y = 1(x - 0)^3 + 0 \][/tex]