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

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, to evaluate ƒ(x) at x = 1/3, you replace x in the function ƒ(x) = -3x + 4 with 1/3, resulting in ƒ(1/3) = -3(1/3) + 4. This process is fundamental in understanding how functions operate and yield results based on different inputs.

Linear Functions

A linear function is a polynomial function of degree one, represented in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. In the given function ƒ(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.

Simplification of Expressions

Simplification of expressions involves reducing mathematical expressions to their simplest form, making them easier to work with. This can include combining like terms, factoring, or reducing fractions. In the context of evaluating functions, after substituting the input value, you may need to simplify the resulting expression to present the final answer clearly and concisely.