options: Define, evaluate, and compare functions.

Analyze functions using different representations.

Build new functions from existing functions.

Understand the concept of a function and use function notation.

Construct and compare linear and exponential models and solve problems.

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

Model periodic phenomena with trigonometric functions.

Prove and apply trigonometric identities.

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

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

Extend the domain of trigonometric functions using the unit circle.
problem_activity: Task
Many computer applications use very complex mathematical algorithms. The faster the algorithm, the more smoothly the programs run. The running time of an algorithm depends on the total number of steps needed to complete the algorithm. For image processing, the running time of an algorithm increases as the size of the image increases.
For an $n$-by-$n$ image, algorithm 1 has running time given by $p(n) = n^3+3n+1$ and algorithm 2 has running time given by $q(n)=15n^2+5n+4$ (measured in nanoseconds, or $10^{-9}$ seconds ).
Compute the running time for both algorithms for images of size 10-by-10 pixels and 100-by-100 pixels.
Graph both running time polynomials in an appropriate window (or several windows if necessary).
Which algorithm is more efficient?


correct_option_index: 1