Algebra 2 = Domain and Range?

Here both Domain and Range are elements of all Real numbers.

Reason:

For every value of 'x', there is a corresponding unique value for 'y'; hence it is a function and domain is all real numbers.

Also no two values of 'x' has the same value for 'y'; hence it is one-one function; hence range is also all real numbers.

You may also do the test in another way:

The graph of this function is a straight line passing through the origin, with slope = Arctan(2), that is an angle of about 63.5 deg. You will observe the graph is through origin and lying only 3rd and 1st quadrants.

Now you can draw any line parallel to y-axis; it will intersect the graph only at one point, as well any line parallel to x-axis also will intersect the graph only at one point. These are all called vertical and horizontal line tests. Since both intersects only at one point and also the graph is from -infinity to +infinity, it is one-one function, Hence both domain and range are elements of all real numbers.

Both the domain and range are (-∞, ∞) or inclusive of all real numbers. Reason being is that there is no value of x for which y wouldn't exist and there's no value of y that doesn't have a related value of x.

To explain a little further, domain is a set of the valid values of x for the function in question. Typically the only time domain will not be (-∞, ∞) is if the x is in the denominator of a fraction (because at some point it will divide by 0) or if the x is under a root symbol (for example √x only exists for x >= 0).

Range is the set of y values that are possible outputs for the function. This will be (-∞, ∞) in the case of any linear equation (y = kx + c where k and c are both constants). It begins to become limited when there is an even exponent (for example y = x² can never have a negative output, same for y = √x).

Thats right... you can put in any x and you'll get an answer. And for the range: Y cannot be greater than 40... because anything squared is positive (or zero), so 40-8x^2 is always 40 (or less), but never greater than 40. So D=all real numbers, R=(-infinity,40] <<(anything less than or equal to 40)