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In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.f(x)=4x+5 a. f(6)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 3, Problema 27b
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)
Guida verificata passo dopo passo1
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).
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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.
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Evaluating Composed Functions
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.
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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.
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06:07Linear Inequalities
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