What is the average rate of change for the sequence shown below?
coordinate plane showing the points 1, 4; 2, 2.5; 3, 1; and 4, negative 0.5

Step-by-step explanation:

The points on the graph are collinear (they lie on one straight line).

Therefore, average of change is the same as a slope.

The formula of a slope:

We choose two points and put the coordinates to the formula

its b

step-by-step explanation:

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: