A variable is a quantity that can change and is not fixed in an analysis. This lets you see how changing one value affects the outcome, like in y = mx + b where x can take different values and y responds accordingly. A constant stays the same within a problem, a unit is just the measurement label (like meters or seconds), and a parameter defines a family of problems but is typically held fixed in a given calculation. So the term that describes a changing quantity most directly is the variable.

For a rational function, the domain excludes points where the denominator is zero. Here the denominator x^2 - 4 factors to (x - 2)(x + 2), which is zero at x = ±2, so all real numbers except ±2 are allowed. At those x-values the numerator x^2 - 1 equals 3, not zero, so the function shoots to infinity there, giving vertical asymptotes at x = ±2. Since both numerator and denominator are degree 2, the end behavior is governed by the ratio of leading coefficients, which is 1, so the horizontal asymptote is y = 1. There are no common factors, so no holes occur. Domain: all real numbers except ±2 Vertical asymptotes: x = ±2 Horizontal asymptote: y = 1

In arithmetic, the result you get when you multiply numbers is called the product. Multiplication combines equal groups to find a total—for example, 3 times 4 gives 12, so 12 is the product of 3 and 4. The other terms map to different operations: sum is what you get when you add numbers, quotient is the result of division, and difference is what you get when you subtract. So the term that matches “the result of multiplying numbers together” is product.

Symmetry is when a figure looks the same after applying a reflection or a rotation. This means the property is unchanged under those transformations. For example, a circle has rotational and reflection symmetry: rotating it by any angle or reflecting across any line through the center leaves it unchanged. A square also has symmetry under 90-degree rotations and under reflections across its axes and diagonals. In this sense, symmetry is the specific term that captures invariant behavior under those geometric transformations, whereas invariance is a broader idea, congruence is about two shapes being the same size and shape, and equivalence is a relational notion not tied to these geometric transformations.