Algebra 2 Unit 5 Test

Front

What is the result of multiplying (x^2 - 2x + 1)(x + 1)?

Back

The result is x^3 - x^2 - x + 1.

Front

What does it mean if the graph of a polynomial function has a relative minimum at (1.18, -1.09)?

Back

It indicates that at x = 1.18, the function reaches a local minimum value of approximately -1.09.

Front

If the graph of a function crosses the x-axis, what can be said about the multiplicity of that zero?

Back

The multiplicity of that zero is odd.

Front

Given f(x) = 2x and g(x) = x^2 + 3, what is f(g(x))?

Back

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

Front

Describe the end behavior of a function where as x approaches infinity, f(x) approaches negative infinity and as x approaches negative infinity, f(x) also approaches negative infinity.

Back

As x → ∞, f(x) → -∞; As x → -∞, f(x) → -∞.

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the degree of a polynomial?

Back

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

Front

What does it mean for a polynomial to have a zero at x = c?

Back

It means that when x = c, the value of the polynomial is zero, indicating that the graph of the polynomial crosses the x-axis at that point.

Front

What is the difference between even and odd functions?

Back

Even functions are symmetric about the y-axis, while odd functions are symmetric about the origin.

Front

How do you find the x-intercepts of a polynomial function?

Back

To find the x-intercepts, set the polynomial equal to zero and solve for x.