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

Verified step by step guidance

1. Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
2. To find ƒ(-3), substitute -3 in place of x in the function ƒ(x).
3. Write the substitution explicitly: ƒ(-3) = -3( -3 ) + 4.
4. Simplify the expression by performing the multiplication and then the addition.
5. Write the simplified expression as the final form of ƒ(-3).

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into the function's formula and calculating the output. For example, to find ƒ(-3), replace x with -3 in ƒ(x) and simplify the expression.

Linear Functions

A linear function has the form ƒ(x) = mx + b, where m and b are constants. It produces a straight-line graph, and evaluating it involves simple arithmetic operations like multiplication and addition.

Quadratic Functions

A quadratic function is a polynomial of degree two, typically written as g(x) = ax² + bx + c. Understanding its structure helps in evaluating the function at given values by substituting and simplifying powers and sums.