Sketch the Graph of the Function $p ( x ) = - ( x + 5 ) ^ { 3 } + 8$

question 83

Essay

Sketch the graph of the function $p ( x ) = - ( x + 5 ) ^ { 3 } + 8$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$ . Indicate all $x$ - and $y$ - intercepts and make sure your graph exhibits the proper end behavior.

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Definitions:

Germinal Stage

The earliest phase of prenatal development, consisting of the first two weeks after conception, during which the zygote begins to divide and implant in the uterine wall.

Embryonic Stage

The period in prenatal development from fertilization until around the end of the eighth week, where significant growth and differentiation of the embryo occurs.

Teratogen

Any agent that can cause developmental malformations (birth defects) in a fetus when exposure occurs during pregnancy.

Environmental Toxins

Harmful pollutants or chemicals present in the environment that can cause adverse health effects on humans and wildlife.