Domain and Range of a Function? HELP!!?

Question

The question is "What is the domain and range of the function "x^4+y=42". The carat symbolizes the 4 is an exponent.

I have the domain I think. (neginf, 42] right? How do I find the range?

Answer 1

Solve the equation for y to find the domain.

x^4 + y = 42

y = 42 - x^4

The domain is all possible x values.  Since you can always raise a number to the fourth power so the domain is (-∞, ∞).

The function is shaped like a parabola which opens downward.  So the range (possible y values) will be from -∞ to some constant which is the maximum of the function.  From the equation y = 42 - x^4.  Since x^4 is always positive, the maximum occurs when x = 0.  Then y = 42.  So the range is (-∞, 42].  

Hope this helps you!