Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(x+2)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. In this case, evaluating ƒ(x+2) means replacing every instance of x in the function ƒ(x) with (x+2). This process is essential for finding the value of the function at a new input.

Linear Functions

A linear function is a polynomial function of degree one, which can be expressed in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. The function ƒ(x) = -3x + 4 is linear, indicating that its graph is a straight line. Understanding the properties of linear functions helps in analyzing their behavior and transformations.

Algebraic Simplification

Algebraic simplification is the process of reducing expressions to their simplest form by combining like terms, factoring, or applying arithmetic operations. After evaluating ƒ(x+2), it may be necessary to simplify the resulting expression to make it easier to interpret or use in further calculations. Mastery of simplification techniques is crucial in algebra.