Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(0)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value into a function to determine its output. For example, to evaluate ƒ(0) for the function ƒ(x) = -3x + 4, you replace x with 0, resulting in ƒ(0) = -3(0) + 4 = 4. This process is fundamental in understanding how functions behave at particular points.

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. 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.

Simplification of Expressions

Simplification involves reducing mathematical expressions to their simplest form. This can include combining like terms, factoring, or reducing fractions. In the context of evaluating functions, simplification ensures that the final answer is presented in the most concise and understandable manner, which is essential for clarity in mathematical communication.