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 function given: \( f(x) = -4x + 2 \).
2. Substitute \( x = -2 \) into the function: \( f(-2) = -4(-2) + 2 \).
3. Calculate \(-4(-2)\), which involves multiplying \(-4\) by \(-2\).
4. Add the result from the multiplication to 2.
5. The expression \( f(-2) = -4(-2) + 2 \) simplifies to a single value.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. In this case, to find ƒ(-2) for the function ƒ(x) = -4x + 2, you replace x with -2, allowing you to calculate the corresponding output value.

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. The function ƒ(x) = -4x + 2 is linear, indicating that its graph is a straight line with a slope of -4 and a y-intercept of 2.

Substitution

Substitution is a fundamental algebraic technique where a variable in an expression is replaced with a specific value. In the context of the given function, substituting -2 for x allows us to compute the output of the function, demonstrating how changes in input affect the output.