What You Will Practice
Pre-calculus brings together algebra, functions, exponents, radicals, polynomial behavior, and basic trigonometry. These skills prepare students for college algebra, pre-calculus, technical math, and calculus readiness.
Mini Lesson
1. Functions
A function connects each input to exactly one output. If the same input gives two different outputs, the relation is not a function.
Example: 2 → 5 and 2 → 7 is not a function because input 2 has two outputs.
2. Function Evaluation
To evaluate a function, substitute the given input value into the rule.
Example: If f(x) = x² - 4x + 3, then f(2) = 2² - 4(2) + 3 = -1.
3. Exponent Rules
When multiplying powers with the same base, add the exponents.
Example: x³ · x² = x⁵
4. Radicals
A square root asks: what number squared gives this value?
Example: √49 = 7 because 7² = 49.
5. Polynomial Evaluation
Substitute the value of x into the polynomial and follow the order of operations.
Example: g(x) = 3x - 1, g(5) = 3(5) - 1 = 14.
6. Basic Trigonometry
In a right triangle, sine and cosine are ratios of side lengths.
Interactive Pre-Calculus Practice
Choose a topic and practice with instant feedback. For exponent answers, type them like x^5.
For decimals, round to two decimal places if needed.
function or not a function.
Use exponent format like x^5. For trig, type the decimal or fraction shown by the ratio.
Mastery Check
Before moving to Chapter 6, students should be able to do the following.
Functions
I can tell whether each input has exactly one output.
Evaluation
I can substitute a value into a function or polynomial.
Exponents
I can multiply or divide powers with the same base.
Radicals
I can simplify basic square roots.
Trigonometry
I can calculate sine or cosine from right-triangle side lengths.