Answer :
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]
- [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]
