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Describe the end behavior of f(x)=1-3x

User Villeaka
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The end behavior of a function describes how the function behaves as x approaches positive or negative infinity. To determine the end behavior of f(x) = 1 - 3x, we can look at the leading term, which is -3x.

As x becomes very large (either positive or negative), the value of -3x becomes very large in the opposite direction. That is, as x approaches positive infinity, -3x approaches negative infinity, and as x approaches negative infinity, -3x approaches positive infinity.

Since the constant term 1 does not have any effect on the end behavior, we can conclude that the function f(x) = 1 - 3x decreases without bound as x approaches positive infinity and increases without bound as x approaches negative infinity.

In other words, the end behavior of f(x) = 1 - 3x can be described as:

As x → ∞, f(x) → -∞

As x → -∞, f(x) → +∞

User Allen Walker
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