Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(-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 = -3, you replace x in the function ƒ(x) = -3x + 4 with -3, resulting in ƒ(-3) = -3(-3) + 4.

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 this case, ƒ(x) = -3x + 4 is a linear function with a slope of -3 and a y-intercept of 4, indicating a straight line when graphed.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form by combining like terms and performing arithmetic operations. 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.