Question

For the function $$ f(x)=-x^{2}+4 $$ a student claimed that $f(-2)=8 .$ This is incorrect. WHAT WENT WRONG? Find the correct value of $f(-2)$.

    For the function
$$
f(x)=-x^{2}+4
$$
a student claimed that $f(-2)=8 .$ This is incorrect. WHAT WENT WRONG? Find
the correct value of $f(-2)$.

Algebra for College Students

Algebra for College Students

Margaret L. Lial,… 9th Edition

Chapter 4, Problem 7

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Step 1

Step 1: We are given the function $f(x)=-x^{2}+4$ and we are asked to find the value of $f(-2)$. Show more…

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For the function $$ f(x)=-x^{2}+4 $$ a student claimed that $f(-2)=8 .$ This is incorrect. WHAT WENT WRONG? Find the correct value of $f(-2)$.

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Key Concepts

Function Evaluation

Evaluating a function requires substituting the input value into the function's expression and then carrying out the arithmetic according to the expression's structure. In this case, the correct approach involves replacing x with -2 and carefully performing the operations as defined in the function formula.

Order of Operations

The order of operations dictates that exponents are calculated before multiplications or additions. For the expression -x^2 + 4, this means that when x is replaced with -2, the square should be computed first (so (-2)^2 becomes 4) and then the negative sign is applied. Misapplying this rule can lead to errors like treating -(-2^2) as -(-4), which results in an incorrect value.

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