College Prep

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Use the vertical line test: if a vertical line intersects the graph of the relation at more than one point, it is not a function.

The domain is the set of all possible input values (x-values) for which the function is defined.

The range is the set of all possible output values (y-values) that a function can produce.

The expression simplifies to $$a + b$$ when @@a eq b@@.

The quadratic formula is $$x = \frac{-b \text{±} \text{√}(b^2 - 4ac)}{2a}$$ , used to find the roots of a quadratic equation $$ax^2 + bx + c = 0$$ .

To evaluate an expression means to calculate its value by substituting the variables with specific numbers.

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

The maximum or minimum value of a quadratic function $$f(x) = ax^2 + bx + c$$ occurs at the vertex, which can be found using $$x = -\frac{b}{2a}$$ .

Factoring a polynomial involves rewriting it as a product of its factors, which can help in solving equations.