Provide an Appropriate Response $f ( x ) = \frac { x - 4 } { x ^ { 2 } - 9 }$

question 167

Multiple Choice

Provide an appropriate response.
-Which function has no vertical asymptote? Why? a. $f ( x ) = \frac { x - 4 } { x ^ { 2 } - 9 }$
b. $f ( x ) = \frac { 2 } { x ^ { 2 } - 6 x }$
c. $f ( x ) = \frac { 3 x ^ { 2 } + 15 } { x ^ { 2 } + 6 }$
d. $f ( x ) = \frac { x + 5 } { ( x - 5 ) ( x - 3 ) }$

• A) b. The numerator is never equal to 0.
• B) d. No factor from the denominator cancels out.
• C) a. The degree of the denominator is larger than the degree of the numerator.
• D) c. The denominator is never equal to 0.

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Definitions:

Bone Mineral

Inorganic substances, primarily hydroxyapatite crystals, that give bones their hardness and strength.

Hydrostatic Skeleton

A hydrostatic skeleton is a structure found in many soft-bodied animals, consisting of a fluid-filled cavity surrounded by muscles, providing support and facilitating movement.

Antagonistically

In a manner that indicates mutual opposition or contradictory actions, often involving biochemical substances or muscles.

Troponin

A regulatory protein complex involved in muscle contraction, found in the muscle fibers, and sensitive to calcium concentrations.