Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(-7/3)

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 = -7/3, you replace x in the function ƒ(x) = -3x + 4 with -7/3, allowing you to calculate the corresponding output value.

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, indicating a straight line when graphed, with a slope of -3 and a y-intercept of 4.

Simplification of Expressions

Simplification of expressions involves reducing mathematical expressions to their simplest form. This can include combining like terms, factoring, or performing arithmetic operations. In the context of evaluating ƒ(-7/3), simplification may be necessary to present the final answer in a clear and concise manner.