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Answer:
2 equivalent expressions w/ negative signs in different places.
a) =-1/5 x and x/-5
b) =14/-y and -14/1/y
c) =a/1/b and 1/b/1/a
d) =-c/y and -c/1/y
The quadratic regression equation that best fits the data set is y = 32.86x² - 379.14x + 1369.14
<h3>The data points </h3>The following table of values represents the data points that would be used to solve this question:
x 3 4 5 6 7 8 9
y 470 416 403 226 314 338 693
Where:
- x represents years since 2000
- y represents the annual revenue of a manufacturing company in thousand dollars
The table of values illustrates a quadratic function.
The function would be calculated using a graphing calculator
From the graphing calculator, we have:
a = 32.86; b = -379.14 and c = 1369.14
A quadratic regression equation is represented as:
y = ax² + bx + c
So, we have:
y = 32.86x² - 379.14x + 1369.14
Hence, the quadratic regression equation that best fits the data set is y = 32.86x² - 379.14x + 1369.14
<h3>Why the function type was chosen?</h3>From the table of values in (a), we can see that as x increases; the value of y decreases and then increases after it reaches a minimum.
This illustrates the behavior of a quadratic regression function
See attachment for the scatter plot
Read more about quadratic regression equation at:
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Answer:
The range of the function is:
Range R = {14, 17, 20}
Step-by-step explanation:
Given the function
We also know that range is the set of values of the dependent variable for which a function is defined.
In other words,
- Range refers to all the possible sets of output values on the y-axis.
We are given that the domain of the function is:
Domain D = {4, 5, 6}
Now,
substituting x = 4 in the function
f(4) = 3(4) + 2
f(4) = 12 + 2
f(4) = 14
substituting x = 5 in the function
f(5) = 3(5) + 2
f(5) = 15 + 2
f(5) = 17
substituting x = 6 in the function
f(6) = 3(6) + 2
f(6) = 18 + 2
f(6) = 20
Thus, we conclude that:
at x = 4, y = 14
at x = 5, y = 17
at x = 6, y = 20
Thus, the range of the function is:
Range R = {14, 17, 20}