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.