Let ƒ(x)=-3x+4 and g(x)=-x^2+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 function's expression. This process is fundamental in algebra as it allows you to compute specific outputs based on given inputs.

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, while the y-intercept is 4, showing where the line crosses the y-axis. Understanding linear functions is crucial for analyzing their behavior and graphing them.

Quadratic Functions

A quadratic function is a polynomial function of degree two, generally represented as g(x) = ax^2 + bx + c. In the function g(x) = -x^2 + 4x + 1, the leading coefficient is negative, indicating that the parabola opens downward. Quadratic functions are important in algebra for modeling various real-world scenarios and understanding their properties, such as vertex and intercepts.