Fill in the blank(s) to correctly complete each sentence. For the function ƒ(x) = -4x + 2, ƒ(-2)= ______.

Verified step by step guidance

1. Identify the given function: \(f(x) = -4x + 2\).
2. Substitute the input value \(x = -2\) into the function to find \(f(-2)\).
3. Replace \(x\) with \(-2\) in the expression: \(f(-2) = -4(-2) + 2\).
4. Simplify the multiplication part: calculate \(-4 \times (-2)\).
5. Add the result from the multiplication to 2 to find the value of \(f(-2)\).

Key Concepts

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula to find the corresponding output. For example, to find ƒ(-2), replace x with -2 in the expression ƒ(x) = -4x + 2 and simplify.

Linear Functions

A linear function is a function whose graph is a straight line, typically expressed as ƒ(x) = mx + b, where m is the slope and b is the y-intercept. Understanding this form helps in quickly evaluating and interpreting the function.

Substitution Method

The substitution method is a technique where a specific value replaces the variable in an expression or equation. This method is essential for evaluating functions at particular points, as it allows direct computation of the output.