Algebra Class: Equations and Functions

Equation of a Line

• Find the equation of a line given a point and slope using the point-slope form: y - y₁ = m(x - x₁), where (x₁, y₁) is the point and m is the slope.
• Example: A line passes through (2, 2) with a slope of -3. The equation is y - 2 = -3(x - 2).

Slope and Y-intercept

• Find the slope and y-intercept of a linear equation in the form Ax + By = C.
• Example: For 2x + 5y = 19, the slope is -2/5 and the y-intercept is 19/5.

Domain and Range of a Function

• Find the domain and range of a quadratic function.
• Example: For y = x² - 5, the domain is all real numbers (-∞, ∞) and the range is y ≥ -5.

Piecewise Function

• Graph a piecewise-defined function by plotting points according to the defined conditions.
• Example: For f(x)= {x+1 if x ≤ 0, x if x > 0}, graph the sections separately for x ≤ 0 and x > 0.

Function Composition

• Find the composition of two functions (g(f(x))).
• Example: If f(x) = -6x + 4 and g(x) = 2x + 7, then g(f(x)) = -12x + 15.

Test your understanding of key algebraic concepts, including finding equations of lines, determining slopes and intercepts, and analyzing domains and ranges of functions. This quiz will also cover piecewise functions and function compositions through example problems.