The domain is the set of all x-values that lead to a range value (y-value). In other words, it’s the set of all acceptable x-values. The range is the set of all y-values produced from the domain values. You can think of the domain as how far left or right the function goes, and the range as how far up and down the function goes.
Looking at the parabola, we see that it extends left and right to negative and positive infinity, hence the arrows at at the “tails” of the function.
So, the domain (D) is:
D: (-∞, ∞)
Note: we use ( ) because infinity is not a defined number, so it’s not a starting point nor end point.
The vertex is where the lowest or highest point of the parabola, so this is where the lowest or highest range value is found. Looking at the parabola’s vertex, 1 is the y-coordinate. So, the highest point the parabola reaches is y=1. It extends all the way down to negative infinity, hence the arrows at the “tails” of the function.
So, the range (R) is:
R: [1, -∞)
Note: we use [ for 1 because it is a defined endpoint since it is the y-coordinate of the vertex.
Hope that helps! I like your name btw!