Variables and CoVariation

Quantitative Reasoning

Quantitative Reasoning: Units and Estimates

We develop our quantitative reasoning skills through units, estimations, and asking ‘does that make sense’?

Quantitative Reasoning: Percents

We practice communicating mathematical explanations through fractions and percents.

Relations and Graphs

Relations and Graphs: Cartesian Coordinates

We plot points on a 2-dimensional Cartesian graph.

Relations and Graphs: Relations

We define relations and graph examples of relations.

Relations and Graphs: Famous Functions

We list important relations and functions that will be explored throughout this course and used often in Calculus.

Changing in Tandem

Changing in Tandem

We explore how mathematics, and graphs in particular, allow us to describe and investigate the relationships between two variables changing in tandem.

Comparing Lines and Exponentials

Linear Equations

Linear Equations: Finding Patterns

We introduce linear equations by finding patterns in tables.

Linear Equations: Slope

We explore the slope of lines.

Linear Equations: Equations of Lines

We explore the different ways we might write the equation of a line including the slope-intercept form, the point-slope form, and standard form.

Linear Modeling

Linear Modeling

We explore how real-world applications of linear equations.

Exponential Modeling

Exponential Modeling: Exponent Rules

We review the rules of exponents.

Exponential Modeling: Early Exponentials

We use exponents when exploring real world situations.

Functions

What is a Function?

What is a Function?

Representations of Functions

Function Properties

Even and Odd Functions

Periodic Functions

Inverse Functions

Famous Function Properties

Average Rate of Change of Functions

Average Rate of Change

Building New Functions

Building New Functions

Algebra of Functions

Composition of Functions

We explore how when can combine two functions by composing them. That is, how we can plug one function into another to create a new function.

Quadratics

Definition of Quadratics

We explore quadratic functions.

Vertex Form

We explore the vertex form of a quadratic.

Factored Form

We explore different methods for solving quadratic functions.

Polynomials

Polynomial Functions

We explore polynomial functions.

Roots

Roots

Exponential Functions Revisited

Introduction to Function Transformations

Vertical and Horizontal Shifts

Stretching Functions

Exponential Functions Revisited

Exponential Functions

Modeling with Exponential Functions Revisited

The Special Number e

Introduction to Logarithms

Definition of Logarithms

Rational Functions

Rational Functions

The Famous Function f(x) = 1∕x

The Definition of a Rational Function

Polynomial Long Division

Properties of Rational Functions

End Behavior of Rational Functions

Zeros of Rational Functions

We find the zeros of a rational function.

Graphing Rational Functions

Domain

Domain

We return to the notion of a function and examine the allowable inputs.

Range

We examine the outputs that are actually achieved.

Famous Functions, Updated

Back Matter


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