Ch. 3 - Polynomial and Rational Functions

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

Blitzer 8th Edition

Ch. 3 - Polynomial and Rational Functions

문제 84

4장, 문제 84

Exercises 82–84 will help you prepare for the material covered in the next section. Let f(x)=an(x⁴−3x²−4). If f(3)=−150, determine the value of a_n.

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Start with the given function:

f (x) = a n (x^{4} - 3 x^{2} - 4)

Substitute

x = 3

into the function to use the given value

f (3) = - 150

. This gives:

-150 = a n (3^{4} - 3 3^{2} - 4)

Calculate the powers of 3 inside the parentheses:

3^{4} = 81

and

3^{2} = 9

Simplify the expression inside the parentheses:

81 - 3 	imes 9 - 4

. Perform the multiplication and subtraction step-by-step.

After simplifying the parentheses, solve for

a n

by dividing both sides of the equation by the simplified value inside the parentheses.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Evaluation

Function evaluation involves substituting a specific input value into the function's expression to find the corresponding output. In this problem, you substitute x = 3 into f(x) to find f(3), which helps in solving for the unknown coefficient a_n.

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole-number exponents combined using addition, subtraction, and multiplication. Understanding the structure of the polynomial f(x) = a_n(x^4 − 3x^2 − 4) is essential to correctly substitute values and manipulate the equation.

Solving for an Unknown Coefficient

When a function includes an unknown coefficient, you can find its value by using given function values. Here, knowing f(3) = -150 allows you to set up an equation and solve for a_n by isolating it after substituting x = 3 into the polynomial.

Exercises 82–84 will help you prepare for the material covered in the next section. Let f(x)=an(x4−3x2−4). If f(3)=−150, determine the value of a_n.