AP Precalculus Section 1.12 Example: Transformations and Domain and Range

Random AP Precalculus Problems (I found on the Internet). These are not official AP Collegeboard examples, but they will definitely get the job done!

- **Vertical Dilation/Stretch**: A vertical dilation (or stretch) of a function f(x) by a factor "a" results in the new function g(x) = a * f(x). It vertically stretches or compresses the graph of f(x) depending on whether "a" is greater than 1 (stretch) or between 0 and 1 (compression).

- **Horizontal Dilation/Compression**: A horizontal dilation (or compression) of a function f(x) by a factor "b" results in the new function g(x) = f(bx). It affects the graph's width and shape. If "b" is greater than 1, it compresses horizontally; if between 0 and 1, it stretches horizontally.

- **Horizontal Translation**: A horizontal translation of f(x) by "c" units to the right is represented as g(x) = f(x - c). It shifts the graph "c" units to the right. To shift left, use "x + c."

- **Vertical Translation**: A vertical translation of f(x) by "d" units upward is represented as g(x) = f(x) + d. It shifts the graph "d" units upward. To shift downward, use "f(x) - d."

These transformations modify the position, shape, and size of the original function's graph, allowing you to create various transformations of the same underlying function.

The Topics covered in AP Precalculus are...

1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
1.4 Polynomial Functions and Rates of Change
1.5 Polynomial Functions and Complex Zeros
1.6 Polynomial Functions and End Behavior
1.7 Rational Functions and End Behavior
1.8 Rational Functions and Zeros
1.9 Rational Functions and Vertical Asymptotes
1.10 Rational Functions and Holes
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.12 Transformations of Functions
1.13 Function Model Selection and Assumption Articulation
1.14 Function Model Construction and Application
2.1 Change in Arithmetic and Geometric Sequences
2.2 Change in Linear and Exponential Functions
2.3 Exponential Functions
2.4 Exponential Function Manipulation
2.5 Exponential Function Context and Data Modeling
2.6 Competing Function Model Validation
2.7 Composition of Functions
2.8 Inverse Functions
2.9 Logarithmic Expressions
2.10 Inverses of Exponential Functions
2.11 Logarithmic Functions
2.12 Logarithmic Function Manipulation
2.13 Exponential and Logarithmic Equations and Inequalities
2.14 Logarithmic Function Context and Data Modeling
2.15 Semi-log Plots
3.1 Periodic Phenomena
3.2 Sine, Cosine, and Tangent
3.3 Sine and Cosine Function Values
3.4 Sine and Cosine Function Graphs
3.5 Sinusoidal Functions
3.6 Sinusoidal Function Transformations
3.7 Sinusoidal Function Context and Data Modeling
3.8 The Tangent Function
3.9 Inverse Trigonometric Functions
3.10 Trigonometric Equations and Inequalities
3.11 The Secant, Cosecant, and Cotangent Functions
3.12 Equivalent Representations of Trigonometric Functions
3.13 Trigonometry and Polar Coordinates
3.14 Polar Function Graphs
3.15 Rates of Change in Polar Functions

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa . #math #shorts #funny #help #onlineclasses #onlinelearning #online #study