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2 years ago

Describe the end behavior of the graph of f(x) = x3(x + 3)(–5x + 1) using limits.

Mathematics

1 answer:

Hitman42 [59]2 years ago

4 0

The end behavior of the graph of f(x) = x3(x + 3)(–5x + 1) using limits is as x ⇒ ∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ ∝

<h3>How to determine the end behavior of the graph of f(x) = x3(x + 3)(–5x + 1) using limits?</h3>

The equation of the function is given as:

f(x) = x^3(x + 3)(–5x + 1)

Using limits, we have:

As x approaches positive infinity, the function becomes

f(∝) = (∝)^3(∝ + 3)(–5(∝) + 1)

Evaluate the products and exponents

f(∝) = (∝)(∝)(–∝ + 1)

Evaluate the difference

f(∝) = (∝)(∝)(–∝)

Evaluate the product

f(∝) = -∝

This means that as x ⇒ ∝, f(x) ⇒ -∝

Using limits, we have:

As x approaches negative infinity, the function becomes

f(-∝) = (-∝)^3(-∝ + 3)(–5(-∝) + 1)

Evaluate the products and exponents

f(-∝) = (-∝)(-∝)(∝ + 1)

Evaluate the sum

f(-∝) = (-∝)(-∝)(∝)

Evaluate the product

f(-∝) = ∝

This means that as x ⇒ -∝, f(x) ⇒ ∝

Hence, the end behavior of the graph of f(x) = x3(x + 3)(–5x + 1) using limits is as x ⇒ ∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ ∝

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