# What is the domain and range of #y =x^2 - 3#?

graph{x^2-3 [-10, 10, -5, 5]}

Domain: (negative infinity, positive infinity)

Range: [-3, positive infinity)

Draw two arrows on the parabola's two edges.

Find the lowest x-value using the graph I've given you. Proceed left and search for a stopping point that isn't possibly the infinite range of low x-values. The lowest y-value is negative infinity.

Now take the highest x-value and determine whether the parabola stops anywhere. It might be (2,013, 45) or some other value, but for the purposes of this discussion, we'll use positive infinity to make things easier on you.

Since (low x-value, high x-value) make up the domain, you have (negative infinity, positive infinity).

NOTE: a soft bracket, not a brace, is required for infinities.

Now, determining the lowest and highest y-values will determine the range.

The parabola stops at a -3 and does not go any lower when you move your finger around the y-axis; this is the lowest range.

Given that -3 is an integer, you would place a brace before the number [-3, positive infinity]. Now, move your finger towards the positive y-values; if you move in the arrows' directions, it will be positive infinity.

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Domain: All real numbers Range: y ≥ -3

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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