Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
2. Graphs of Equations
Graphs and Coordinates
1:33 minutes
Problem 27
Textbook Question
Textbook QuestionIn Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.f(x)=4x+5 b. f(x + 1)
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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, to evaluate f(x + 1), we replace x in the function f(x) = 4x + 5 with (x + 1). This process allows us to determine the output of the function for a given input.
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Algebraic Simplification
Algebraic simplification is the process of reducing an expression to its simplest form. After substituting (x + 1) into the function, we will perform operations such as distribution and combining like terms to simplify the resulting expression. This step is crucial for presenting the final answer clearly.
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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 helps in visualizing and interpreting the results of function evaluations.
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