Key Algebra 1 Concepts

Key Algebra 1 Concepts

• Independent Variable: The controllable input letter in an equation or function.

• Dependent Variable: The output letter, which responds to the independent variable.

• Slope: Represents the rate of change in a linear relationship; calculated as rise over run, or change in y divided by change in x.

• X-intercept: The point(s) where a graph intersects the x-axis; occurs when y equals zero.

• Y-intercept: The point(s) where a graph crosses the y-axis; occurs when x equals zero.

• Domain: The set of all possible independent variable values (x-values) for a function; read a graph from left to right.

• Range: The set of all possible dependent variable values (y-values) for a function; read a graph from bottom to top.

• Function: A relationship where each input (x) has a unique output (y); verified by the vertical line test.

• Linear Function: A function that graphs as a straight line and has a constant slope.

• Quadratic Function: A function involving x, typically represented in a standard form such as ( ax^2 + bx + c ).

• Exponential Function: A function where each term represents a constant factor or multiple relative to previous terms.

• Inverse Variation: The relationship where the product of two variables equals a constant; mathematically expressed as ( xy = k ) or ( y = \frac{a}{x} ).

• Inequalities: Statements that show the relative size or order of two values; multiplying or dividing by a negative number reverses the inequality direction.

• Distributive Property: A principle stating that multiplying a term by a sum or difference inside parentheses means applying that term to each element within, e.g., ( a(b+c) = ab + ac ).

• Value of a Function: Refers to substituting a specific number into the function’s equation in place of the independent variable.

• Transformations of ( y = x^2 + c ): Changes in the graph's shape based on the value of "a" (steeper or wider) and position due to "c" (upward or downward shift).

• Exponent Rules:

  • Multiplying like bases requires adding exponents.
  • Dividing like bases requires subtracting exponents.
  • Any variable raised to the zero power equals one.
  • When raising a power to another power, multiply the exponents.

• Parallel Lines: Lines that run in the same direction, having identical slopes yet differing y-intercepts; they never meet.

• Perpendicular Lines: Lines that intersect at a right angle (90 degrees); their slopes are opposite reciprocals of one another.

This quiz covers fundamental concepts in Algebra 1, including independent and dependent variables, slope, intercepts, domain, and range. Test your understanding of these essential terms and their relationships within linear functions. It's perfect for high school students looking to solidify their algebra knowledge.