QQuestionMathematics
QuestionMathematics
"End Behavior of Polynomial Functions
Identify the leading coefficient and degree of the polynomial function f(2$)= 5x^2 + 7x−3.
• Degree: 2
• Leading Coefficient: 5
• End Behavior: As x→∞, f(2$)→∞; as x→−∞, f(2$)→∞"
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Answer
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Step 1:: Identify the leading coefficient and degree of the polynomial function.
The given polynomial function is $f(x) = 5x^2 + 7x - 3$.
Step 2:: Determine the degree of the polynomial function.
In this polynomial, the highest power of the variable $x$ is 2.
Therefore, the degree of the polynomial function is 2.
Step 3:: Determine the leading coefficient of the polynomial function.
The coefficient attached to the term with the highest power of the variable is called the leading coefficient. In this case, the leading coefficient is 5.
Step 4:: Describe the end behavior of the polynomial function.
• As $x \to -\infty$, $f(x) \to \infty$
We can write this mathematically as:
Final Answer
• Degree: 2 • Leading Coefficient: 5 • End Behavior: As $x \to \infty$, $f(x) \to \infty$; as $x \to -\infty$, $f(x) \to \infty$
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