Hello from MrBillDoesMath!
Answer:
All real x
Discussion:
Take any real number, say, P. Then solve
f(x) = (x-2)2 + 2 = P => (subtract 2 from both sides)
(x-2)2 = P -2 => (divide both sides by 2)
(x-2) = (1/2) (P-2) => (add 2 to both sides)
x = (1/2)(P-2) + 2
Conclusion: for any real number range value, P, there is an x (given by the above formula) such that f(x) = P. In other words, the range of f is all real numbers x
Regards,
MrB
To convert 2.77777777777 to a fraction:
Assume x = 2.7777777777......equation 1
Now, notice that the repeating digit is 7
multiply both sides of the equation by 10:
10x = 27.7777777777.......equation 2
Subtract equation 1 from equation 2 as follows:
10x - x = 27.7777777777 - 2.7777777777
9x = 25
Therefore x = 25/9
Based on this, 2.7 repeated can be written as a fraction = 25/9
so these two lines intersect at x = 3 hmmmm what's the y-coordinate of the second line at that point?
so the y-coordinate of that second line is 0, so the point there is (3, 0) then.
so the first line is, a line that has a slope of 2 and passes through (3, 0).