Functions and Polynomials Flashcard

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

Front

What does it mean for y to be a function of x?

Back

For y to be a function of x, each value of x must correspond to exactly one value of y. This means that no x-value can map to multiple y-values.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the input variable into the function's equation and simplify.

Front

What is the process of factoring an expression?

Back

Factoring an expression involves rewriting it as a product of its factors, which can help simplify or solve equations.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, such as a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 3x^4 + 2x^2 + 1, the degree is 4.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a degree of 1 and graphs as a straight line, while a quadratic function has a degree of 2 and graphs as a parabola.