At what point is the vertex? Is it a minimum or maximum?
(-2,7);maximum
(-1,0);minimum
(2,-9);minimum
(0,-5);minimum
(2,-9);maximum
(4,-5);maximum

(2, -9); minimum

Step-by-step explanation:

The vertex is the point that either has the largest y value (maximum) or it has the smallest y value (minimum). It is also the point on the graph where if it's a maximum, all the points to the left and right of it are less than it and if it's a minimum, all the points to the left and right of it are more than it.

Looking at the table, we see that the smallest y value is -9. The values beside it are -5 and -8, where are both greater than -9. So, this is a very potential candidate for minimum.

The largest y value is 7. We can't see all the values beside it, but we can guess from the trend, that the y values on one side will be more. So, it can't be a maximum.

Thus, the vertex is at the minimum (2, -9).

Hope this helps!

(2,-9);minimum

Step-by-step explanation:

Since the data is symmetrical about x = 2,

Vertex is (2, -9)

On both sides of x = 2, the y values are greater than -9. Therefore it's a minimum point

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

i hope this is what you were looking for.

see attached graph