Algebra Mid-Chapter 2 Review

Domain and Range

• The domain of a set of ordered pairs consists of the first elements: {1, 3, 5, 7}.
• The range consists of the second elements from the same set: {2, 4, 6, 8}.

Function Evaluation

• For the function f(x) = -3x + 2:
  • f(4) results in -10.
  • f(0) results in 2.
  • f(-a) results in 3a + 2.

Linearity

• The equation 3x + 4y = 12 is classified as linear.
• The equation y = x³ - 6 is classified as nonlinear.

Standard Form

• The equation -4y = 3x - 24 can be rearranged to standard form as 3x + 4y = 24.
• The equation y = 12x can be converted to standard form as 12x - y = 0.

Slope Calculation

• The slope between the points (2, 5) and (6, -3) is calculated as -2.
• The slope between the points (8, 2) and (2, 8) is calculated as -1.

Key Definitions

• The symbol m represents slope.
• The symbol b denotes the y-intercept.

Slope-Intercept Form

• An equation with a slope of -2 through the point (-3, -5) is expressed as y = -2x - 11.
• An equation passing through (-2, 4) and (0, 8) has the form y = 2x + 8.
• A horizontal line with points (3, 5) and (-1, 5) is represented as y = 5.

Relationships Between Slopes

• Parallel lines maintain the same slope.
• Perpendicular lines have slopes that are opposite reciprocals.

Slope of Parallel and Perpendicular Lines

• A line parallel to y = 3x + 5 has a slope of 3.
• A line perpendicular to y = 3x + 5 has a slope of -1/3.