Question

How do I write where f is decreasing in interval notation (comments)?

Answer 1

Hmmm so where does it start decreasing? x=-4?

Answer 2

(-4, 5) and I think (-6, 0) are the points?

Answer 3

(0,-6) for the second one, yah.

Answer 4

Any idea why where do I my HW says (left end point must be less than right end point)?

Answer 5

We would uhhhh say.. that the function is decreasing on (-4,0)

We want to know over which part of the domain the function is decreasing.

Answer 6

So we only list the x-coordinates.

Answer 7

Oh...so (-4,0)?

Answer 8

Ya that's our interval notation.
I can't remember if we use rounded or square brackets for this.
No no rounded sounds right. The function isn't decreasing "AT" -4, just to the right of it.
So we use round to exclude that value.

ok ok ok ya that looks right.

Answer 9

Thank you so much. Seems like it's right. Oh and quickie, what would this mean in interval notation? "{x element R : x<=0 or x>=9}"

Answer 10

Pay attention to the grey boxes I draw, I'll try to give an explanation for each part.
`{` `x∈R` `:` `x<=0` or `x>=9` }

`The set of` `x's in the real numbers` `such that` `x is less than or equal to 0` or `x is greater than or equal to 9` }.

Oh you asked for interval notation.. my bad D:

(-infty, 0] ∪ [ 9, infty )

Square brackets around the 0 and 9 because of the "or equal to" that our inequality is giving.

Answer 11

We always draw round brackets around infinity.
Infinity is not an actual "value", so we can't include it in our interval like we would with a square bracket.