If f(x)=x^2-x, find f(x+h).

Name: Problem 11, Chapter 5: Calculus With Trigonometry and Analytic Geometry
Uploaded: 2022-02-26T22:50:29-08:00
Duration: 1 min 8 s
Channel: Erika Bustos
Description: If f(x)=x^2-x, find f(x+h).

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Key Concepts

Combining Like Terms

After substituting and expanding expressions, combining like terms simplifies the expression to its most compact form. This crucial algebraic process helps in reducing polynomials to a form that is easier to interpret or use in further calculations.

Function Notation and Evaluation

Function notation is the mathematical representation of a function's rule, such as f(x) = x² - x, where input values are mapped to output values. Evaluating the function at a different input, like (x+h), means substituting that entire expression in place of x, which is a fundamental concept in algebra and calculus.

Substitution

Substitution is the process of replacing the variable in a function with another expression. In this problem, x is replaced with x+h in the function f(x), demonstrating how changes in the input affect the output.

Polynomial Expansion

Polynomial expansion involves applying algebraic identities or distributive properties to expand expressions raised to a power. Here, expanding (x+h)² is necessary to write out the function f(x+h) completely.

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