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

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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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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