Fall 2024 Algebra 2 Semester Exam

Front

What is the decreasing interval on a function?

Back

The decreasing interval is the range of x-values where the function's output decreases as x increases. For example, if a function decreases from negative infinity to -3, the decreasing interval is (-∞, -3).

Front

Describe the end behavior of a polynomial function.

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. For example, if as x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞, the function rises on both ends.

Front

How do you find the composition of functions f(g(x))?

Back

To find f(g(x)), first evaluate g(x) for a specific x-value, then substitute that result into f(x). For example, if f(x) = 2x and g(x) = 2x^2 - 1, then f(g(3)) = f(2(3)^2 - 1) = f(17) = 34.

Front

What are natural numbers?

Back

Natural numbers are the set of positive integers starting from 1, 2, 3, and so on. They do not include zero or negative numbers.

Front

What is the vertex of a quadratic function in vertex form?

Back

The vertex of a quadratic function in the form y = a(x-h)^2 + k is the point (h, k). For example, in y = (x-3)^2 + 5, the vertex is (3, 5).

Front

What is the definition of a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. For example, f(x) = 2x^3 - 3x + 5 is a polynomial function.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers (e.g., 1/2, 3, -4), while irrational numbers cannot be expressed as a simple fraction (e.g., √2, π).

Front

How do you determine the x-intercepts of a function?

Back

To find the x-intercepts of a function, set the function equal to zero and solve for x. The solutions are the x-values where the graph crosses the x-axis.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0 and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of a quadratic equation. If it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.