Algebra 2 2-6 Families of Functions

Problem 1 Got It? How are the functions related?

Problem 1 Got It? How are the graphs of the functions related?

Problem 1 Got It? Graph the functions on the same coordinate plane. Zoom and pan your graph to leave an appropriate scale and viewing window. After graphing, you may edit your responses to the previous 2 items.

Problem 2 Got It? Consider the projectile altitude f(x) of the airplane shown in Problem 2. Suppose the flight leaves 30 minutes early. What function represents this transformation?

Problem 4 Got It? For the function f(x) shown in Problem 4 and in the table below, what is the corresponding table for the transformation h(x)? Complete the table for h(x) on the canvas. Use a color other than black.

Problem 4 Got It? Reasoning: If several transformations are applied to a graph, will changing the order of transformations change the resulting graph? Explain.

Compare and Contrast: Part A: The graph below shows f(x) = 0.5x - 1.

Graph g(x) by translating f(x) up 2 units and then stretching it vertically by the factor 2.

Compare and Contrast: Part B: The graph below shows f(x) = 0.5x - 1.

Graph h(x) by stretching f(x) vertically by the factor 2 and then translating it up 2 units.

Reasoning: Can you give an example of a function for which a horizontal translation gives the same resulting graph as a vertical translation? Explain.

Analysis: Find a new function g(x) transformed from f(x) = -x - 2 such that g(x) is perpendicular to f(x).

Review Lesson 2-5: A musician's manager keeps track of the ticket prices and the attendance at recent performances in the table above.

Step 1. Use the embedded Desmos graphing utility above or visit desmos.com to create a scatterplot and to calculate and graph the line of best fit for the given data.

Step 2. Take a screenshot of your scatterplot and line of best fit.

Step 3. Upload your screenshot to the canvas below.

If you need a reminder of how to complete Step 1, review this video from the Desmos team and/or see Problem 3 from the Lesson 2-5 slideshow.

Review Lesson 1-6: Resequence the items below to indicate the correct procedure for solving the absolute value equation.

1. Isolate the |x - 3| part of the expression by subtracting 2 from each side of the equation.
2. Check both possible solutions by substituting them into the original equation, |x - 3| + 2 = 7.
3. Separate the equation |x - 3| = 5 into two equations: x - 3 = 5 and x - 3 = -5.
4. Solve the two equations separately to find two possible solutions: x = 8 and x = -2.
5. Since both solutions satisfy the equation, they are both solutions of the equation.

Review Lesson 1-6: Fill in the blank: When solving absolute value equations, a possible solution that does not check out when substituted into the equation is called a(n) __?__.

Vocabulary Review: Identify the items that are NOT vertical.

Use Your Vocabulary: Complete each statement with the correct form of the word translation.

Reflection: Math Success