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

Prove and apply trigonometric identities.

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

Extend the domain of trigonometric functions using the unit circle.

Build new functions from existing functions.

Model periodic phenomena with trigonometric functions.

Construct and compare linear and exponential models and solve problems.

Analyze functions using different representations.

Understand the concept of a function and use function notation.

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

Define, evaluate, and compare 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: 7

9