What is the domain and range of #y=x^2#?

Question

Genesis Allen · Accepted Answer

The graph of this equation (as well as a function) should be familiar to us: plot{x^2 [-20.19, 20.36, -2.03, 18.25]} The domain is the set of all allowed #x# values.  Although it is not 100% certain from the graph, it is clear from the equation, that for any number you put in for #x# you will get one and only one value for #y#.  The domain is all real numbers .  (The interval #(-oo, oo)#)  The range is the set of all #y# value the graph actually includes. Looking at the graph (and thinking about #x^2#, it becomes clear that #y# will never have a negative value.
It is not 100% certain from the graph, but every number that is NOT negative will be used as a #y# value.  The range is #[0, oo)#

Isaiah Anthony · Answer

undefined Domain: All real numbers (negative infinity to positive infinity)
Range: All real numbers greater than or equal to zero (zero to positive infinity)

HIX Tutor · Answer

undefined To find the domain and range of $y = x^2$:

**Domain:**
1. Look at all the possible values for $x$.
2. You can use any number (positive, negative, or zero).
3. So, the domain is all real numbers: $(-∞, ∞)$.

**Range:**
1. Look at the possible values for $y$.
2. Since $x^2$ is always zero or positive (it never goes below zero).
3. So, the smallest value of $y$ is 0, and it can go up to infinity.
4. Therefore, the range is $[0, ∞)$.

**Summary:**
- Domain: $(-∞, ∞)$
- Range: $[0, ∞)$