Translations of Functions Unit 3. Are you ready to slide? Sing along if you know it!

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Presentation transcript:

Translations of Functions Unit 3

Are you ready to slide? Sing along if you know it!

What is a transformation? I Translations –A) Move Up –B) Move Down –C) Move Left –D) Move Right –E) Combinations of A – D II Reflections –A) Reflect about the x-axis (Upside-Down) III Distortions –A) Vertical Stretch (Steeper) –B) Vertical Compression (Flatter) –C) Horizontal Stretch (Wider) –D) Horizontal Compression (Narrower)

Let’s investigate on the calculator 1) Graph y = x –This original function, often called the parent function, will be our “starting” graph. 2) Now graph y = x + 2 –What did you notice happened to the graph? 3) Now graph y = x – 3 –What did you notice happened to the graph? 4) Can you generalize what happens when we have numbers at the end of a function rule? Test a few more values on your calc.

Vertical Translations A Vertical Translation is a shift of a function in a vertical direction (up or down). These are represented as f(x) + k, where k is the amount of movement. Starting from y = x, how could we show a vertical translation 5 units up? Starting from y = x, if I wanted to move the graph 9 units down, what should I write?

More calculator explorations 1) Graph y = |x| (absolute value function) –This original function, often called the parent function, will be our “starting” graph. 2) Now graph y = |x + 2| –What did you notice happened to the graph? –Is this what you expected? Why? 3) Now graph y = |x – 3| –What did you notice happened to the graph? 4) Can you generalize what happens when we have numbers inside of a function rule? Test a few more values on your calculator.

Horizontal Translations A Horizontal Translation is a shift of a function in a horizontal direction (left or right) These are represented as f(x – h), where h is the amount of movement Starting from y = |x|, how could we show a horizontal translation 7 units left? Starting from y = |x|, if I wanted to move the graph 4 units right, what should I write?

Video Time Our translation activity follows, so pay close attention to how he moves the graphs. A visual explanation of translations, with algebra thrown in for fun!A visual explanation of translations, with algebra thrown in for fun!

Translations Activity Each pair will receive one picture of a function and one graphing overhead film; Each quad will receive overhead pens In black, copy the main function f(x) from the paper picture onto your overhead film In blue, sketch f(x) + 2 on the same graph In red, sketch f(x – 3) on the same graph In green, sketch f(x +1) – 2 on the same graph Each pair will have 10 minutes to complete this activity; sharing to follow

For your notes… Can we relate Domain and Range to these function translations? Take a look at the function to the right. Copy this into your notes. List the domain and range of the given function, h(x). Now graph h(x) – 3 in a different color. What do you notice about the domain and range of the new graph? Now graph h(x + 1) in a third color. What do you notice about the domain and range of the new graph?

Closure Everyone stand up and form two large circles, one inside the other. Inside circle faces out, outer circle faces in. Pair up with the person opposite you. Take turns sharing things you learned today until each person has shared twice. Don’t forget the HW – have a great weekend!