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

Build a function that models a relationship between two quantities.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.

Understand the concept of a function and use function notation.

Prove and apply trigonometric identities.

Use functions to model relationships between quantities.

Build new functions from existing functions.

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

Analyze functions using different representations.

Extend the domain of trigonometric functions using the unit circle.

Model periodic phenomena with trigonometric functions.
problem_activity: Task
Suppose $P_1 = (0,5)$ and $P_2 = (3,−3)$. Sketch $P_1$ and
$P_2$. For which real numbers $m$ and $b$ does the graph of a linear function described by the equation $f(x) = mx+b$ contain $P_1$? Explain. Do any of these graphs also contain $P_2$? Explain.
Suppose $P_1 = (0,5)$ and $P_2 = (0,7)$.  Sketch $P_1$ and $P_2$.  Are there real numbers $m$ and $b$ for which the graph of a linear function described by the equation $f(x)=mx+b$ contains $P_1$ and $P_2$? Explain.
Now suppose $P_1= (c,d)$ and $P_2 = (g,h)$ and $c$ is not equal to $g$. Show that there is only one real number $m$ and only one real number $b$ for which the graph of $f(x)=mx+b$ contains the points $P_1$ and $P_2$.


correct_option_index: 2

4