Precalculus Midterm

Front

What is an even function?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain. Example: f(x) = x^2.

Front

What is an odd function?

Back

A function f(x) is odd if f(-x) = -f(x) for all x in the domain. Example: f(x) = x^3.

Front

What does it mean for a function to have a zero?

Back

A zero of a function f(x) is a value x such that f(x) = 0.

Front

How do you determine if k is a zero of f(x)?

Back

Substitute k into f(x) and check if the result is 0.

Front

What is function composition?

Back

Function composition is applying one function to the result of another. If f(x) and g(x) are functions, then f(g(x)) is their composition.

Front

How do you find f(g(x)) for f(x) = 2x and g(x) = x^2 + 3?

Back

f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero is the number of times that zero appears as a root of the function.

Front

How do you find the real zeros of a polynomial function?

Back

Set the polynomial equal to zero and solve for x.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.