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SIZIF [17.4K]
2 years ago
14

HElP Me PLEASE

Mathematics
1 answer:
Georgia [21]2 years ago
7 0

Answer:

As x → -∞, f(x) → 0.5; as x → ∞, f(x) → 0.5

Step-by-step explanation:

Given function:

f(x)=\dfrac{4x-7}{8x+8}

<u>Asymptote</u>: a line that the curve gets infinitely close to, but never touches.

As the degrees of the numerator and denominator of the given function are equal, there is a horizontal asymptote at  y=\dfrac{a}{b}  (where a is the leading coefficient of the numerator, and b is the leading coefficient of the denominator).  This is the end behavior.

\textsf{Horizontal asymptote}:y=\dfrac{4}{8}=\dfrac{1}{2}

This is because as x \rightarrow \infty the -7 of the numerator and the +8 of the denominator become negligible.  Therefore, we are left with:

f(x) \rightarrow \dfrac{4x}{8x}

Therefore:

\textsf{As }\:x \rightarrow - \infty, f(x) \rightarrow 0.5

\textsf{As }\:x \rightarrow \infty, f(x) \rightarrow 0.5

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