Functions Unit Review

Relations and Functions Define relation and function

Compare and Contrast the two

Create a series of points that are a function and one that is not. Note the domain and range in each.

Create an equation that is a function and one that is not. Note the domain and range in each.

Create a graphic representation of two functions and two relations. Note the domain and range in each.

Determine the Domain and Range

= y y=

Linear Relationships and Functions

Given the following 2 situations determine if the relationship is linear or not. Then express the situation as a table, graph, and as a equation in slope-intercept form and functional notation.

If the relationship is exponential in nature create a recursive function instead, then convert the recursive to explicit.

Situation AMaking Bread

Audrey is making bread. The recipe calls for 1 tsp. of yeast mixed with warm water. She hears phone ring so she goes to answer it. As she chats on her phone the amount of yeast grows to triple its current amount every ten minutes.

Situation BShip Traffic - Concordia

A cargo ship left the Oregon coast headed for Australia approximately three days ago. The weather has been very rough and the ship navigator notes that they have only traveled 80 nautical miles while the storm raged outside. The ship normally averages 22 knots, which is nautical miles per hour. (5 nautical miles – 5.8 miles) The ship captain asks if they continue the rest of the journey at average speeds how much farther do they need to travel. He asks the navigator this same question at least three times a day for the rest of the trip. It is 7660 miles from Oregon to Australia.

Catching up

A second cargo ship, Dyna, decides to wait to leave the Oregon coast until after the storm has passed. It is bigger and faster than Concordia, traveling at an average of 28 knots. This ship captain asks his navigator how long it will be until they catch up with Concordia if they travel at average speeds.

Ape arm length – the following data shows the relationship for a species. Create a linear equation that best fits the data.

Comparing representations Determine which has the largest rate of change

F(x) = ¾x + 4x y

-6 10 53 7

Given each situation explain what changes would occur 

  If f(x) = what would happen to the equation and graph

when: f(x) + k , where k = -15 ?

If f(x) = 4x +10 what would happen to the graph when: k=-1 in the transformation of k*f(x) ?

You and your friend each purchased identical subscriptions to an online video rental site. When you joined, you each paid the one-time membership processing fee. You also paid a flat rate for each movie that you downloaded. By the end of the first month, you had downloaded 8 movies and paid $16.50, while your friend had downloaded only 6 movies and paid $14.00. Determine the membership fee and the flat fee per movie.

Systems of Equations

There are ________ types of solutions for a system of equations problem: ________________________________________________________________________

Write and graph an example of each type of solution for different system of equations problems

System of Linear Inequalities

Graph the system of linear inequalities. Determine the point of intersection and choose 2 points that lie in the solution set.

f(x) > x - 12 and g(x) <

Given each recursive function create an explicit function that passes through a specific point.

Interpret parts of an expression