SOLUTION: 7. y = x2 + 86 A. Domain = {all real numbers}, Range = {all real numbers < 86} B. Domain = {all real numbers}, Range = {all real numbers >= 86} C. Domain = {all real numbers},

Algebra ->  Functions -> SOLUTION: 7. y = x2 + 86 A. Domain = {all real numbers}, Range = {all real numbers < 86} B. Domain = {all real numbers}, Range = {all real numbers >= 86} C. Domain = {all real numbers},      Log On


   

Question 1197778: 7. y = x2 + 86
A. Domain = {all real numbers}, Range = {all real numbers < 86}
B. Domain = {all real numbers}, Range = {all real numbers >= 86}
C. Domain = {all real numbers}, Range = {all real numbers}
D. Domain = {all real numbers}, Range = {all real numbers <= 1}
E. Domain = {all real numbers <= 1}, Range = {all real numbers <= 86}
F. Domain = {all real numbers > 1}, Range = {all real numbers}

8. y = 2x3 + 8
A. Domain = {all real numbers}, Range = {all real numbers}
B. Domain = {all real numbers}, Range = {all real numbers > 8}
C. Domain = {all real numbers}, Range = {all real numbers >= 8}
D. Domain = {all real numbers}, Range = {all real numbers <= 8}
E. Domain = {all real numbers <= 2}, Range = {all real numbers <= 8}
F. Domain = {all real numbers > 2}, Range = {all real numbers}
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Problem 7

The domain is the set of all real numbers because we can plug in any real number for x to get some output for y.
There aren't any restrictions to worry about. We don't have to worry about division by zero errors for instance, or stuff like square roots of negative numbers.

The range is the set of real numbers such that y+%3E=+86
This is because the smallest x%5E2 can get is 0, which means the smallest x%5E2%2B86 can get is 0%2B86+=+86
So either y = 86 or y > 86.

The graph shows how y = 86 is the lowest we can go on this parabola.
graph%28400%2C400%2C-5%2C10%2C80%2C90%2C0%2Cx%5E2%2B86%29
I recommend using the graphing tool Desmos, GeoGebra, or similar to plot this curve out. That way you can interact with it to adjust the window and such.

Answer: choice B
domain = all real numbers
range = y%3E=86

====================================================

Problem 8

Like with the previous problem, the domain is the set of all real numbers. This domain applies to any polynomial.

However, the range will be different this time.
The range of any cubic is the set of all real numbers. Any output is possible. We have no min value, nor max value. Notice the graph stretches upward and downward forever.
graph%28400%2C400%2C-5%2C5%2C-3%2C15%2C0%2C2x%5E3%2B8%29

Answer: choice A
domain = all real numbers
range = all real numbers