Algebra II - Semester 1 Exam

Front

What is the Domain?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, for the function f(x) = x^2, the domain is all real numbers, denoted as (-∞, ∞).

Front

Find the inverse of f(x) = x^2 - 4.

Back

The inverse function is f^{-1}(x) = \sqrt{x + 4}. This is found by solving the equation y = x^2 - 4 for x.

Front

What is the range of the function represented by the set {-4, 0, 1, 3}?

Back

The range of a function is the set of all possible output values (y-values). In this case, the range is {-4, 0, 1, 3}.

Front

Write the transformed function that shifts the parent function ƒ(x) = |x| up 2 units.

Back

The transformed function is ƒ(x) = |x| + 2.

Front

Solve the system of linear equations: 2x + 3y = 1 and x - y = 4.

Back

The solution to the system is (-3, -1).

Front

What is a function's inverse?

Back

A function's inverse reverses the effect of the original function. If f(x) takes x to y, then f^{-1}(y) takes y back to x.

Front

Define the term 'range' in relation to functions.

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 to transform a function?

Back

Transforming a function involves shifting, stretching, compressing, or reflecting the graph of the function.

Front

How do you find the domain of a function?

Back

To find the domain, identify all x-values that do not cause the function to be undefined, such as division by zero or taking the square root of a negative number.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|, which produces a V-shaped graph.