Algebra Unit 1 and 2 basics

Inequality by Negative Number

The inequality sign flips.

Midpoint Formula

(x1 + x2)/2, (y1 + y2)/2.

Distance Formula

(x2 - x1)² + (y2 - y1)².

Vertical Line Test

To check if a graph represents a function.

Domain and Range Difference

Domain = valid x-values (inputs), Range = valid y-values (outputs).

Average Rate of Change Formula

(f(x2) - f(x1)) / (x2 - x1).

Difference Quotient Formula

(f(x + h) - f(x)) / h.

Function Composition Formula

(f ∘ g)(x) = f(g(x)).

Effect of -f(x)

Reflects the graph across the x-axis.

Effect of f(-x)

Reflects the graph across the y-axis.

Effect of f(x) + c

Shifts the graph up (if +c) or down (if -c).

Effect of f(x + c)

Shifts the graph left (if +c) or right (if -c).

Effect of a f(x) when |a| > 1

Vertical stretch.

Effect of a f(x) when 0 < |a| < 1

Vertical shrink.

Effect of f(ax) when |a| > 1

Horizontal shrink.

Effect of f(ax) when 0 < |a| < 1

Horizontal stretch.

Steps for Solving Quadratic Inequalities

Factor → find zeros → test intervals → pick solution set.

Steps for Solving Rational Inequalities

Set numerator and denominator = 0 → make sign chart → test intervals → pick valid solution.