In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.f(x)=4x+5 b. f(x + 1)

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: Substitute (x + 1) into the function in place of 'x'. This means replacing every occurrence of 'x' in the function with (x + 1). The new expression becomes f(x + 1) = 4(x + 1) + 5.

Step 3: Apply the distributive property to simplify 4(x + 1). Multiply 4 by both 'x' and '1', resulting in 4x + 4.

Step 4: Combine like terms. Add the constant terms 4 and 5 together to simplify the expression further. This gives f(x + 1) = 4x + 9.

Step 5: The simplified expression for f(x + 1) is now f(x + 1) = 4x + 9. This is the final simplified form of the function evaluated at (x + 1).

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, to evaluate f(x + 1), you replace x in the function f(x) = 4x + 5 with (x + 1). This process allows you to find the output of the function for a new input.

Algebraic Simplification

Algebraic simplification is the process of reducing an expression to its simplest form. After substituting x + 1 into the function, you will need to simplify the resulting expression, combining like terms and performing any necessary arithmetic operations to achieve a clearer representation of the function's output.

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 is essential for evaluating and interpreting their behavior.