Which graph shows a rate of change of one-half between –4 and 0 on the x-axis? On a coordinate plane, a straight line with a positive slope crosses the x-axis at (6, 0) and the y-axis at (0, 3). Solid circles appear on the line at (negative 4, negative 1), (0, 3). On a coordinate plane, a parabola opens up. It goes through (negative 5.25, 4), has a vertex of (0, negative 3), and goes through (5.25, 4). Solid circles appear on the parabola at (negative 4, 1), (0, negative 3). On a coordinate plane, a parabola opens down. It goes through (negative 5.5, negative 4), has a vertex of (0, 4), and goes through (5.5, negative 4). Solid circles appear on the parabola at (negative 4, 0), (0, 4). On a coordinate plane, a curved line opens up and left in quadrant 2. It is asymptotic to the negative x-axis and positive y-axis. Solid circles appear on the line at (negative 4, 0.25), (0, 4).

First option

Step-by-step explanation:

There is a mistake in the description of the first function.  

On a coordinate plane, a straight line with a positive slope crosses the x-axis at (-6, 0) and the y-axis at (0, 3). Solid circles appear on the line at (-4, 1), (0, 3).

Given two points of a function, (x1, y1) and (x2, y2), its rate of change between them is:

Rate of change: (y2 - y1)/(x2 - x1)

Points of the 1st graph: (-4, 1), (0, 3).

Rate of change: (3- 1)/(0 - (-4)) = 1/2

Points of the 2nd graph: (-4, 1), (0, -3).

Rate of change: (-3 - 1)/(0 - (-4)) = -1

Points of the 3rd graph: (-4, 0), (0, 4).

Rate of change: (4 - 0)/(0 - (-4)) = 1

Points of the 4th graph: (-4, 0.25), (0, 4).

Rate of change: (4 - 0.25)/(0 - (-4))   = 0.9375

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: