Math 3 NC Check In #1

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to whole number powers and coefficients, combined using addition, subtraction, and multiplication.

Front

If (x + 5) is a factor of a polynomial, what does that imply about the polynomial's value at x = -5?

Back

The polynomial's value at x = -5 must be zero.

Front

What is the range of a function?

Back

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

Front

What does it mean if a function is increasing on an interval?

Back

A function is increasing on an interval if, as the input values (x) increase, the output values (y) also increase.

Front

What is the domain of a function?

Back

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

Front

What does it mean for a root to have a multiplicity of 2?

Back

A root with a multiplicity of 2 means that the graph of the polynomial touches the x-axis at that root but does not cross it.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function as x approaches positive or negative infinity.

Front

How do you determine if (x + 2) is a factor of a polynomial?

Back

You can use polynomial long division or synthetic division to check if the remainder is zero when dividing by (x + 2).

Front

What does it mean for a function to have a positive leading coefficient?

Back

A polynomial function with a positive leading coefficient will rise to positive infinity as x approaches positive infinity.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.