In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.f(x)=4x+5 c. f(-x)

검증된 단계별 안내

Step 1: Start with the given function f(x) = 4x + 5. This is a linear function where 'x' is the independent variable.

Step 2: To evaluate f(-x), substitute '-x' in place of 'x' in the function. This means replacing every occurrence of 'x' in the expression with '-x'.

Step 3: After substitution, the function becomes f(-x) = 4(-x) + 5.

Step 4: Simplify the expression by distributing the 4 to '-x'. This results in f(-x) = -4x + 5.

Step 5: The simplified expression for f(-x) is f(-x) = -4x + 5. This is the final simplified form of the function when evaluated at -x.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function. In this case, we replace 'x' in the function f(x) = 4x + 5 with -x to find f(-x). This process allows us to determine the output of the function for different inputs.

Simplification

Simplification is the process of reducing an expression to its simplest form. After evaluating the function at f(-x), we will combine like terms and eliminate any unnecessary components to present the result in a clear and concise manner. This step is crucial for clarity and ease of understanding.

Linear Functions

A linear function is a polynomial function of degree one, which can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. The function f(x) = 4x + 5 is linear, indicating that its graph is a straight line. Understanding the properties of linear functions helps in analyzing their behavior and transformations.