Variables and CoVariation

1Quantitative Reasoning

1.1Quantitative Reasoning: Units and Estimates

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

1.2Quantitative Reasoning: Percents

We practice communicating mathematical explanations through fractions and percents.

2Relations and Graphs

2.1Relations and Graphs: Cartesian Coordinates

We plot points on a 2-dimensional Cartesian graph.

2.2Relations and Graphs: Relations

We define relations and graph examples of relations.

2.3Relations and Graphs: Famous Functions

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

3Changing in Tandem

3.1Changing 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

4Linear Equations

4.1Linear Equations: Finding Patterns

We introduce linear equations by finding patterns in tables.

4.2Linear Equations: Slope

We explore the slope of lines.

4.3Linear 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.

5Linear Modeling

5.1Linear Modeling

We explore how real-world applications of linear equations.

6Exponential Modeling

6.1Exponential Modeling: Exponent Rules

We review the rules of exponents.

6.2Exponential Modeling: Early Exponentials

We use exponents when exploring real world situations.

Functions

7What is a Function?

7.1What is a Function?

7.2Representations of Functions

8Function Properties

8.1Even and Odd Functions

8.2Periodic Functions

8.3Inverse Functions

8.4Famous Function Properties

9Average Rate of Change of Functions

9.1Average Rate of Change

Building New Functions

10Building New Functions

10.1Algebra of Functions

10.2Composition 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.

11Quadratics

11.1Definition of Quadratics

We explore quadratic functions.

11.2Vertex Form

We explore the vertex form of a quadratic.

11.3Factored Form

We explore different methods for solving quadratic functions.

12Polynomials

12.1Polynomial Functions

We explore polynomial functions.

13Roots

13.1Roots

Exponential Functions Revisited

14Introduction to Function Transformations

14.1Vertical and Horizontal Shifts

14.2Stretching Functions

15Exponential Functions Revisited

15.1Exponential Functions

15.2Modeling with Exponential Functions Revisited

15.3The Special Number e

16Introduction to Logarithms

16.1Definition of Logarithms

Rational Functions

17Rational Functions

17.1The Famous Function f(x) = 1∕x

17.2The Definition of a Rational Function

17.3Polynomial Long Division

18Properties of Rational Functions

18.1End Behavior of Rational Functions

18.2Zeros of Rational Functions

We find the zeros of a rational function.

18.3Graphing Rational Functions

19Domain

19.1Domain

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

19.2Range

We examine the outputs that are actually achieved.

19.3Famous Functions, Updated

Back Matter


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