Select the correct answer from each drop-down menu. The graph of the equation y = -x4 + x2 − 2
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)

The graph of the equation y = x5 + x2 + 7
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)

The graph of the equation y = x6 + 2x3 + 3
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)

y = -x⁴ + x² - 2 : D

y = x⁵ + x² + 7 : B

y = x⁶ + 2x³ + 3 : C

Step-by-step explanation:

anyways look at the part with the largest power of x. it will have the biggest impact on the overall value, when x approaches positive or negative infinity.

in the first one this is -x⁴

x⁴ is always positive (for positive and negative x). so, -x⁴ is always negative. therefore, it decreases in both cases when x approaches positive or negative infinity.

in the second one this is x⁵.

this goes with the sign of x. it is getting bigger (it increases), when x approaches positive infinity, and it is getting smaller (it decreases), when x approaches negative infinity.

in the third one this is x⁶.

this is always positive (for positive and negative x). therefore, it increases in both cases when x approaches positive or negative infinity.

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:

answer: howdy

step-by-step explanation: