Equations, Exponents & Graphs

Front

What is the process of factoring polynomials?

Back

Factoring polynomials involves breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial. For example, 125x³ - 216 can be factored as (5x - 6)(25x² + 30x + 36).

Front

Define continuity in the context of graph analysis.

Back

Continuity refers to a function being unbroken or uninterrupted over its domain. A function is continuous if you can draw its graph without lifting your pencil. If there are breaks, jumps, or holes, the function is discontinuous.

Front

What does it mean for a function to be discontinuous?

Back

A function is discontinuous if there are points in its domain where the function does not have a defined value or where there are jumps or breaks in the graph. Types of discontinuities include infinite, jump, and removable.

Front

What is symmetry in graph analysis?

Back

Symmetry in graph analysis refers to the property of a graph being identical on either side of a line (axis) or point. Common types include x-axis symmetry, y-axis symmetry, and origin symmetry.

Front

How do you simplify polynomial expressions?

Back

To simplify polynomial expressions, combine like terms and arrange the terms in standard form (from highest degree to lowest). For example, 5y(y⁵ + 8y³) simplifies to 5y⁶ + 40y⁴.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is expressed as a sum of terms in descending order of their degrees. For example, 3x² + 2x + 1 is in standard form.

Front

What is the domain of a function?

Back

The domain of a function is the complete set of possible values (inputs) for which the function is defined. For example, for the function f(x) = 1/(x+3), the domain excludes x = -3.

Front

What is the range of a function?

Back

The range of a function is the complete set of possible output values (y-values) that the function can produce. For example, the range of f(x) = x² is [0, ∞) since it cannot produce negative values.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

What is the significance of the x-intercept in graphing?

Back

The x-intercept is the point where the graph crosses the x-axis, indicating the value of x when y = 0. It is important for understanding the roots of the function.