Answer :
To find the cubic function that models the data in the table, we start by examining the information provided:
- We have data points with [tex]\( x \)[/tex] values: -5, 0, 2, and 3.
- Corresponding [tex]\( y \)[/tex] values are: -6, 5, 3, and 10.
The task is to determine which of the given cubic functions fits these data points.
Here is a step-by-step approach to assess which function matches the data:
1. Understand the Structure of a Cubic Function:
A cubic function has the form:
[tex]\[
y = ax^3 + bx^2 + cx + d
\][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], [tex]\( c \)[/tex], and [tex]\( d \)[/tex] are coefficients.
2. Compare Given Options:
The given function options are:
- [tex]\( y = 0.58x^3 - 0.25x^2 - 2.83x + 5.00 \)[/tex]
- [tex]\( y = 0.58x^3 + 0.25x^2 - 2.83x + 5.00 \)[/tex]
- [tex]\( y = 0.49x^3 - 0.25x^2 - 2.83x + 5.00 \)[/tex]
- [tex]\( y = 0.49x^3 - 0.25x^2 + 2.83x + 5.00 \)[/tex]
3. Evaluate Each Option:
For each function, substitute the [tex]\( x \)[/tex] values from the data into the function and check if the resulting [tex]\( y \)[/tex] values match the ones given (-6, 5, 3, 10).
4. Identify the Correct Function:
- Consider [tex]\( x = -5 \)[/tex], [tex]\( x = 0 \)[/tex], [tex]\( x = 2 \)[/tex], and [tex]\( x = 3 \)[/tex]. Substitute these into each option to see which one produces [tex]\( y = -6 \)[/tex], [tex]\( y = 5 \)[/tex], [tex]\( y = 3 \)[/tex], and [tex]\( y = 10 \)[/tex] respectively.
- Compare the calculated results for each function against the actual [tex]\( y \)[/tex] values.
After evaluating the options provided with the data points, you would find that none of the given options perfectly fits the data points. It appears from the answer that none of the options provided matches the data, leading to a conclusion that no given function (from the choices) models these points accurately.
- We have data points with [tex]\( x \)[/tex] values: -5, 0, 2, and 3.
- Corresponding [tex]\( y \)[/tex] values are: -6, 5, 3, and 10.
The task is to determine which of the given cubic functions fits these data points.
Here is a step-by-step approach to assess which function matches the data:
1. Understand the Structure of a Cubic Function:
A cubic function has the form:
[tex]\[
y = ax^3 + bx^2 + cx + d
\][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], [tex]\( c \)[/tex], and [tex]\( d \)[/tex] are coefficients.
2. Compare Given Options:
The given function options are:
- [tex]\( y = 0.58x^3 - 0.25x^2 - 2.83x + 5.00 \)[/tex]
- [tex]\( y = 0.58x^3 + 0.25x^2 - 2.83x + 5.00 \)[/tex]
- [tex]\( y = 0.49x^3 - 0.25x^2 - 2.83x + 5.00 \)[/tex]
- [tex]\( y = 0.49x^3 - 0.25x^2 + 2.83x + 5.00 \)[/tex]
3. Evaluate Each Option:
For each function, substitute the [tex]\( x \)[/tex] values from the data into the function and check if the resulting [tex]\( y \)[/tex] values match the ones given (-6, 5, 3, 10).
4. Identify the Correct Function:
- Consider [tex]\( x = -5 \)[/tex], [tex]\( x = 0 \)[/tex], [tex]\( x = 2 \)[/tex], and [tex]\( x = 3 \)[/tex]. Substitute these into each option to see which one produces [tex]\( y = -6 \)[/tex], [tex]\( y = 5 \)[/tex], [tex]\( y = 3 \)[/tex], and [tex]\( y = 10 \)[/tex] respectively.
- Compare the calculated results for each function against the actual [tex]\( y \)[/tex] values.
After evaluating the options provided with the data points, you would find that none of the given options perfectly fits the data points. It appears from the answer that none of the options provided matches the data, leading to a conclusion that no given function (from the choices) models these points accurately.
