Algebra 10: Jafna línu og hrings

Equation of a Line

• Describes the representation of a straight line in a graph.
• The formula is y = mx + b.
• m indicates the slope (direction of the line), determining if it rises or falls.
• b is the y-intercept, indicating where the line crosses the y-axis.

Equation of a Circle

• Defines the graphical representation of a circle.
• The formula is (x - h)² + (y - k)² = r².
• (h, k) represents the center of the circle.
• r is the radius, measuring the distance from the center to any point on the circumference.

Translation and Scaling of Graphs

• Translation shifts the graph horizontally or vertically without altering its shape.
• Scaling enlarges or reduces the size of the graph, affecting its dimensions but not its structure.

Strictly Decreasing and Increasing Functions

• An increasing function rises as x increases.
• A decreasing function falls as x increases.
• Strictly implies that these behaviors consistently occur without exceptions.

Even and Odd Functions

• An even function has symmetry across the y-axis, appearing identical on both sides.
• An odd function displays rotational symmetry about the origin, flipping at the ends.

Polynomials; Division, Factoring, and Roots

• Polynomials consist of several terms, e.g., x² + 3x + 2.
• Methods like division and factoring are used to discover roots.
• Roots are the specific values that result in the equation equating to zero.

Absolute Value Function

• The absolute value function measures the distance of a number from zero.
• It is always non-negative, denoted as |x|; for instance, |−3| = 3.

Triangle Inequality

• States that the sum of any two sides of a triangle is always greater than the third side.
• This principle establishes limits on the possible lengths of triangle sides.

Sign Function (sgn(x))

• Determines whether a number is positive, negative, or zero.
• Outputs: sgn(x) = 1 if positive, sgn(x) = −1 if negative, and sgn(x) = 0 if zero.