1
What a function is
35 lessonsA rule that gives exactly one output for each input.
1.1Functions as input-output rulesMath 6
1.3Independent and dependent variablesMath 6
1.4Relations and functionsMath 8
1.8Evaluating a function at a numberMath 8
1.9A reasonable domain for a real situationAlgebra 1
1.10Graphing a function from a tableMath 8
1.12Graphs that tell a storyMath 8
1.13Reading values off a graphMath 8
1.15Domain and range
1.16Evaluating a function at an expressionAlgebra 1
1.17Function notation in a real situationAlgebra 1
1.18Domain and range from a graphAlgebra 1
1.19The implied domain of a formulaAlgebra 2
1.21Average rate of change from a formulaAlgebra 1
1.22Average rate of change from a table or graphAlgebra 1
1.25Intercepts and zeros of a functionAlgebra 1
1.26Symmetry about the vertical axis and the originAlgebra 2
1.27Turning points, maximums and minimumsAlgebra 1
1.28Continuous graphs, jumps and holesAlgebra 2
1.29Solving f(x) = g(x) with graphs and tablesAlgebra 1
1.30End behaviorAlgebra 1
1.31Even and odd functionsAlgebra 2
1.32What an asymptote isAlgebra 1
1.33Concavity: when the rate of change itself changesPrecalculus
1.34Rates at an instant from shrinking intervalsPrecalculus
1.35The difference quotientPrecalculus
2
Linear functions
6 lessonsConstant rate of change, straight-line graph, and modeling with them.
2.5Linear and nonlinear functionsMath 8
2.6Linear functions in contextAlgebra 1
3
Exponential functions
13 lessonsThe variable is in the exponent: growth by a constant factor.
3.3Growth and decay factorsAlgebra 1
3.4Graphs of exponential functionsAlgebra 1
3.6Linear versus exponential growthAlgebra 1
3.8Building an exponential model from two pointsPrecalculus
3.9Doubling time and half lifeAlgebra 2
3.10Compound interest and compounding periodsAlgebra 2
3.11Transforming an exponential graphAlgebra 2
3.12Logistic growth: when growth levels offPrecalculus
3.13The number e and the natural exponential functionAlgebra 2
4
Modeling with functions
6 lessonsChoosing a function family and fitting its numbers so that one rule describes real data.
4.2Choosing a function family for dataAlgebra 1
4.3Building a model from a descriptionAlgebra 1
4.4Interpreting the numbers in a modelAlgebra 1
4.6Judging and comparing modelsPrecalculus
5
Piecewise and absolute value functions
9 lessonsDifferent rules on different stretches of the input.
5.1Evaluating a piecewise functionAlgebra 1
5.2Graphing a piecewise functionAlgebra 1
5.5Step functions and the greatest integer functionAlgebra 1
5.6The absolute value graphAlgebra 1
5.7Writing a piecewise rule from a graphAlgebra 1
5.8Piecewise functions in contextAlgebra 1
5.9Transforming the absolute value graphAlgebra 2
6
Quadratic functions
4 lessonsThe family whose graphs are parabolas, where the output depends on the square of the input.
6.3Quadratic functions in contextAlgebra 1
6.4Reading a quadratic in its three formsAlgebra 1
7
Transformations of functions
11 lessonsShift, flip and stretch a graph by changing the formula.
7.1The identity and constant functionsAlgebra 1
7.3Reflecting a graph across the axesAlgebra 2
7.4Shifting a graph up, down, left and rightAlgebra 2
7.5Stretches and compressionsAlgebra 2
7.6The square root and reciprocal functionsAlgebra 2
7.7The squaring and cubing functionsAlgebra 2
7.9Finding the rule of a transformed graph or tableAlgebra 2
7.10Combining transformations and the general formAlgebra 2
7.11Graphing by transforming a parent graphAlgebra 2
8
Combining and composing functions
6 lessonsFeed one function's output into another.
8.2Adding, subtracting and multiplying functionsAlgebra 2
8.4Composing functions algebraicallyAlgebra 2
8.6Domain of a compositionAlgebra 2
9
Radical functions
4 lessonsThe family whose rule takes a root of the input, with graphs that start at an edge and curve away.
9.1Cube root functions and roots as powersAlgebra 2
9.3Graphing square root functionsAlgebra 2
9.4Radical functions in contextAlgebra 2
10
Inverse functions
6 lessonsSwap input and output; the function that undoes another.
10.1Inverse from a table or list of pairsAlgebra 2
10.3One to one functions and the horizontal line testAlgebra 2
10.4Finding an inverse from a ruleAlgebra 2
10.5Restricting a domain to get an inverseAlgebra 2
10.6The graph of an inverseAlgebra 2
11
Logarithms
12 lessonsThe exponent you need: the inverse of the exponential.
11.1Definition of a logarithmAlgebra 2
11.2Laws of logarithmsAlgebra 2
11.3Logarithms
11.4Solving exponential equations by matching basesAlgebra 2
11.5Evaluating logarithms, common and naturalAlgebra 2
11.6Change of baseAlgebra 2
11.7Expanding and condensing logarithmsAlgebra 2
11.8Solving by taking a logarithm of both sidesAlgebra 2
11.9Logarithmic scalesAlgebra 2
11.10Graphs of logarithmic functionsAlgebra 2
11.11Semi-log plots: straightening exponential data with logarithmsPrecalculus
11.12Solving logarithmic equationsAlgebra 2
12
Polynomial functions
7 lessonsGraphs of polynomials: their shape, their ends, and where they cross zero.
12.3Zeros and multiplicityAlgebra 2
12.4Cubic, quartic and higher degree functionsAlgebra 2
12.5Graphing polynomial functionsAlgebra 2
12.6Modeling with polynomial functionsAlgebra 2
12.7Building a polynomial from its zerosAlgebra 2
13
Rational functions
9 lessonsOne polynomial over another, and the gaps and asymptotes that creates.
13.1Transforming the reciprocal graphAlgebra 2
13.2Domain and zeros of a rational functionAlgebra 2
13.3Asymptotes
13.4Graphing rational functionsAlgebra 2
13.5Horizontal asymptotesAlgebra 2
13.7Rational functions in contextAlgebra 2
13.8Slant asymptotesPrecalculus
13.9Vertical asymptotesAlgebra 2