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Polynomials, EXT1 EQ-Bank 11

A polynomial \(f(x)\) is defined by

\(f(x)=-3x^3+27x^2+12x-1\)

Explain what happens to \(f(x)\) as  \(x \rightarrow-\infty\).   (2 marks)

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\(\text{Since}\ f(x) \ \text{has degree 3:}\)

\(\text{As} \ \ x \rightarrow-\infty, x^3 \rightarrow-\infty\)

\(f(x) \ \text{has leading coefficient}=-3\)

\(\therefore\ \text{As} \ \ x \rightarrow-\infty,-3 x^3 \rightarrow \infty, \ f(x) \rightarrow \infty\)

Show Worked Solution

\(\text{Since}\ f(x) \ \text{has degree 3:}\)

\(\text{As} \ \ x \rightarrow-\infty, x^3 \rightarrow-\infty\)

\(f(x) \ \text{has leading coefficient}=-3\)

\(\therefore\ \text{As} \ \ x \rightarrow-\infty,-3 x^3 \rightarrow \infty, \ f(x) \rightarrow \infty\)

Filed Under: Graphs of Polynomials Tagged With: Band 3, smc-6742-30-\(x \rightarrow \pm \infty\), syllabus-2027

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