What is the range in interval notation of the function graphed below?

Range tells you how high and low the graph of this parabola goes in the “y” (vertical) directions.

1. We can see that the parabola peaks on the y-axis at y = 4. That’s as HIGH as it goes.

2. We also see that both sides of the parabola descend to the level of y = -7. That’s as LOW as it is shown to go.

So putting these together, we say the Range is given by:

-7 <= y <= 3

AMBIGUITY WARNING:
Because the two branches of the parabola go fall right down to the edge of the picture boundary, it’s UNCLEAR whether the parabola truly stops at y = -7 or CONTINUES on (to negative infinity).

In THAT case, the RANGE simplifies to:

Y <= 4

Done.