Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(0)

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Identify the function f(x) given as \(f(x) = -3x + 4\).

To find \(f(0)\), substitute \(x = 0\) into the function \(f(x)\).

Perform the substitution: \(f(0) = -3(0) + 4\).

Simplify the expression by multiplying and adding: \(f(0) = 0 + 4\).

Write the simplified result for \(f(0)\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula and simplifying to find the output. For example, to find f(0), replace x with 0 in f(x) and simplify the expression.

Linear Functions

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. Understanding its structure helps in quickly evaluating the function at any x-value by direct substitution.

Quadratic Functions

A quadratic function is a polynomial of degree two, typically written as g(x) = ax² + bx + c. Evaluating it requires substituting the input value into the expression and simplifying, often involving squaring the input.

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