Question
y =3x^2 + 6
How does the function created from the table below compare to the function above?
x y
1 9
3 15
6 24
8 30
11 39
The equation that the values in the table represent is
, so the table represents
function.
The equation represents
function, because it
have a constant slope.
How does the function created from the table below compare to the function above?
x y
1 9
3 15
6 24
8 30
11 39
The equation that the values in the table represent is
, so the table represents
function.
The equation represents
function, because it
have a constant slope.
Answers
GPT-4o mini
To compare the function \( y = 3x^2 + 6 \) with the values in the table, we need to first determine the function represented by the table.
Let's analyze the values from the table:
- For \( x = 1 \), \( y = 9 \)
- For \( x = 3 \), \( y = 15 \)
- For \( x = 6 \), \( y = 24 \)
- For \( x = 8 \), \( y = 30 \)
- For \( x = 11 \), \( y = 39 \)
Now, let's see if this sequence of \( y \)-values fits a quadratic pattern or is linear by calculating the first and second differences:
**First differences:**
- \( 15 - 9 = 6 \)
- \( 24 - 15 = 9 \)
- \( 30 - 24 = 6 \)
- \( 39 - 30 = 9 \)
First differences: \( 6, 9, 6, 9 \)
**Second differences:**
- \( 9 - 6 = 3 \)
- \( 6 - 9 = -3 \)
- \( 9 - 6 = 3 \)
The first differences are not constant, and the second differences are not constant either, indicating that it doesn't represent a linear function.
We do not yet see a consistent pattern in the differences, so let's check again to see if this function is quadratic by determining a pattern in the y-values in relation to the x-values. We can calculate the possible formula using the points given.
Based on the values, we could use polynomial regression or interpolate using the given points to derive its equation. However, since it appears quite nonlinear, you might confirm that the function could be quadratic.
**The equation that the values in the table represent is not readily determinable from the values provided.** Since the second differences are not constant, we lean towards it being neither purely quadratic.
Thus we can note:
1. The values seem to increase in a nonlinear fashion.
2. Since the differences in y-values are neither uniformly increasing nor decreasing, it is likely that the function is neither truly quadratic nor linear.
To summarize:
- The equation that the values in the table represent may be a quadratic function or could be nonlinear.
- The equation represents a nonlinear function, because it does not have a constant slope.
Thus the completion might be:
1. The equation that the values in the table represent is not clearly defined (could be nonlinear), so the table represents a nonlinear function.
2. The equation represents a nonlinear function because it does not have a constant slope.
Let's analyze the values from the table:
- For \( x = 1 \), \( y = 9 \)
- For \( x = 3 \), \( y = 15 \)
- For \( x = 6 \), \( y = 24 \)
- For \( x = 8 \), \( y = 30 \)
- For \( x = 11 \), \( y = 39 \)
Now, let's see if this sequence of \( y \)-values fits a quadratic pattern or is linear by calculating the first and second differences:
**First differences:**
- \( 15 - 9 = 6 \)
- \( 24 - 15 = 9 \)
- \( 30 - 24 = 6 \)
- \( 39 - 30 = 9 \)
First differences: \( 6, 9, 6, 9 \)
**Second differences:**
- \( 9 - 6 = 3 \)
- \( 6 - 9 = -3 \)
- \( 9 - 6 = 3 \)
The first differences are not constant, and the second differences are not constant either, indicating that it doesn't represent a linear function.
We do not yet see a consistent pattern in the differences, so let's check again to see if this function is quadratic by determining a pattern in the y-values in relation to the x-values. We can calculate the possible formula using the points given.
Based on the values, we could use polynomial regression or interpolate using the given points to derive its equation. However, since it appears quite nonlinear, you might confirm that the function could be quadratic.
**The equation that the values in the table represent is not readily determinable from the values provided.** Since the second differences are not constant, we lean towards it being neither purely quadratic.
Thus we can note:
1. The values seem to increase in a nonlinear fashion.
2. Since the differences in y-values are neither uniformly increasing nor decreasing, it is likely that the function is neither truly quadratic nor linear.
To summarize:
- The equation that the values in the table represent may be a quadratic function or could be nonlinear.
- The equation represents a nonlinear function, because it does not have a constant slope.
Thus the completion might be:
1. The equation that the values in the table represent is not clearly defined (could be nonlinear), so the table represents a nonlinear function.
2. The equation represents a nonlinear function because it does not have a constant slope.