Identifying Parent Functions and Their Transformations

Admin — Sun, 02 Mar 2025 04:12:20 +0000

9.26.F – Discussion #2
We have learned about various parent functions and how to transform them using translations, reflections, compressions, and stretches. In this discussion, you will practice identifying types of functions and the transformations applied to them.
Here is what you will do.
The first person to reply to this discussion will use my function at the bottom of the instructions for Steps 1-3. Each person after that will use the previous student’s function from Step 4. Each person must do all of the following:
Identify the parent function that the function came from. (Make sure you clearly indicate whose function you are referring to.)
Explain each transformation of the function based on the changes in the equation.
Graph the parent function and the transformed function.
Please post your own transformed function (from any of the function families we have learned about) for the next student to use.
Check the solution that the next student posts in response to your function.
Each person uses the previous student’s Step 4 function and identifies, explains, and graphs that function for their own Steps 1-3. For example, I have posted the first function below. Then let’s say Allie is the first to respond. She follows steps 1-3 using the function I have posted, and then she writes her own transformed function in Step 4 for the next student to use. Then Blake follows steps 1-3 using Allie’s function and posts his own transformed function for Step 4. Allie checks Blake’s answer for her function and lets him know if he is correct or not. Then Cal follows steps 1-3 using Blake’s function and posts his own transformed function for Step 4. Blake checks Cal’s answer, and the process continues with each student after that.
If you are not sure about the instructions, please ask.
Post by classmate

Function for the next student to use: h (x) = ( x – 1)^2 + 4

Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!

This discussion requires you to analyze a function, identify its parent function, describe its transformations, and create a new function for the next student. Here’s how to break it down step by step:

Step 1: Identify the Parent Function

Look at the given function:
h(x) = (x – 1)² + 4
Compare it to basic parent functions:

The parent function is f(x) = x², which is a quadratic function (parabola).

Example Answer: The given function h(x) = (x – 1)² + 4 comes from the parent function f(x) = x², which represents a standard quadratic function.

Step 2: Explain the Transformations

You need to describe what happens to the function based on the equation.

(x – 1)² → This represents a horizontal shift to the right by 1 unit.
+ 4 → This represents a vertical shift upward by 4 units.

Example Answer:

The function shifts 1 unit to the right because of the (x – 1) inside the squared term.
The function shifts 4 units up due to the +4 at the end of the equation.
Since there are no reflections, stretches, or compressions, the shape of the parabola remains the same.

Step 3: Graph the Parent and Transformed Functions

Graph f(x) = x² (the standard parabola).
Graph h(x) = (x – 1)² + 4 by applying the transformations.

Graphing Tips:

The parent function f(x) = x² has its vertex at (0,0).
The transformed function h(x) = (x – 1)² + 4 has its vertex at (1,4).
Both graphs open upwards and have the same shape.

Use Desmos or a graphing calculator to visualize the changes!

Step 4: Create a New Function for the Next Student

Choose a transformation from any function family learned in class.
Example: g(x) = -2(x + 3)² – 5

Example Answer:
For the next student, use this function: g(x) = -2(x + 3)² – 5

Step 5: Check the Next Student’s Response

Read their explanation.
Verify if they identified the correct parent function and transformations.
Provide feedback if needed.

By following these clear steps, you’ll complete the discussion effectively. Let me know if you need more help!

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