Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(p)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value into a function to determine its output. For example, if you have a function f(x) and you want to find f(p), you replace x with p in the expression of f. This process is fundamental in understanding how functions behave at different points.

Linear Functions

A linear function is a polynomial function of degree one, typically expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. In the given function f(x) = -3x + 4, the slope is -3, indicating a decrease in value as x increases. Understanding linear functions is crucial for analyzing their graphs and behaviors.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, represented as g(x) = ax² + bx + c. The function g(x) = -x² + 4x + 1 is a downward-opening parabola due to the negative leading coefficient. Recognizing the characteristics of quadratic functions, such as their vertex and axis of symmetry, is essential for solving related problems.