options: Model periodic phenomena with trigonometric functions.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.

Analyze functions using different representations.

Understand the concept of a function and use function notation.

Build a function that models a relationship between two quantities.

Extend the domain of trigonometric functions using the unit circle.

Interpret functions that arise in applications in terms of the context.

Prove and apply trigonometric identities.

Build new functions from existing functions.

Interpret expressions for functions in terms of the situation they model.

Use functions to model relationships between quantities.
problem_activity: Task
Complete the table. In the third column, show your work as demonstrated. What do you notice about the 3rd column?
{"table": [{"tbody": [{"tr": [{"th": [{"_value": "$x$"}, {"_value": "$y=2x+5$"}, {"_value": "$\\Delta y$"}]}, {"td": [{"_value": "1"}, {"_value": "7"}, {"_value": "----"}]}, {"td": [{"_value": "2"}, {"_value": "9"}, {"_value": "9 - 7 = 2"}]}, {"td": [{"_value": "3"}, {}, {}]}, {"td": [{"_value": "4"}, {}, {}]}, {"td": [{"_value": "5"}, {}, {}]}]}]}]}
Complete the table, showing your work as above. What do you notice about the 3rd column? What is the graphical interpretation of this?
{"table": [{"tbody": [{"tr": [{"th": [{"_value": "$x$"}, {"_value": "$y=ax+b$"}, {"_value": "$\\Delta y$"}]}, {"td": [{"_value": "1"}, {"_value": "$a\\cdot\u00a01 +b$"}, {"_value": "---"}]}, {"td": [{"_value": "2"}, {"_value": "$a \\cdot\u00a02 +b$"}, {"_value": "$a\\cdot\u00a02+b - (a\\cdot\u00a01 + b) = a$"}]}, {"td": [{"_value": "3"}, {}, {}]}, {"td": [{"_value": "4"}, {}, {}]}, {"td": [{"_value": "5"}, {}, {}]}]}]}]}
Let $y=ax+b$. Let $x_0$ be any particular $x$-value. Show that if $x_0$ is increased by 1, the corresponding $\Delta y$ is a constant that does not depend on $x_0$. What is this constant?
Does (a) serve as an example of the result in (c) ? Explain.


correct_option_index: 1