Answer:
this is a function
Explanation:
ok so this we will solve with Order of Operations in mind, so first lets take a close look at the problem
y = 2x^{2} - 4x + 5
so since we have different variables on both sides of this equation, the answer isn't completely noticeable
since the right side of the equation is just a variable, lets try to substitute the x variable on the left side with a number, we will go with 3 for this time, so..
y = 2 * 3^{2} - 4 * 3 + 5
now solve for the number with the exponent
(3^{2}) = 9
y = 2 * 9 - 4 * 3 + 5
then following order of operations we will multiply...
2 * 9 = 18
4 * 3 = 12
y = 18 - 12 + 5
then add...
12 + 5 = 17
y = 18 - 17
then subtract...
18 - 17 = 1
y = 1
and VWOLA, when X = 3, Y = 1, but if we changed the value to say... 5, then we would do the problem all over again BUT all x values are = to 5, lets try it
x = 5
y = 2 * 5^{2} - 4 * 5 + 5
(5^{2}) = 25
y = 2 * 25 - 4 * 5 + 5
2 * 25 = 50
4 * 5 = 20
y = 50 - 20 + 5
20 + 5 = 25
y = 50 - 25
50 - 25 = 25
y = 25
and this is proof that this is a function, though it is not a LINIER function because the exponent causes the plotted line to curve on a graph