Learning Objectives:

__Determining Transformations of Functions __

**Vertical Stretch and Vertical Compression**: To **transform **the **function** **f(x) **to **a(b(x+c))** +d. Let's first talk about the value of **"a." y = a f(x), **for** a ˃ 1**, we'll stretch the graph of **f(x)** vertically by a factor of **"a."** **y =a f(x),** for **0 ˂a ˂ 1**, we'll compress the graph of **f(x)** vertically by a factor of **"a."** One way to find coordinates of a **transformed function** in this form would be to find points on the **parent function**, keep the **x** coordinates the same, but multiply the** y** coordinates by **"a"** to find the **y** coordinates of the **transformed function**.

**Horizontal Stretch and Horizontal Compression: **To **transform** the **function** **f(x)** to** a **(**b(x+c)) +d**. Let's first talk about the value of **"b." y = f(b x), **for** b ˃ 1**, we'll compress the graph of **f(x)** horizontally by a factor of **"b."** **y = f(b x), **for** 0 ˂b ˂ 1,** we'll stretch the graph of **f(x)** horizontally . **Reflections over the x-axis and y-axis**: To do the reflection of the function **f(x) **to** a(b(x+c)) +d. y= -f(x) **for** a ˂0** reflects **f(x)** about **x-axis. y= f(-x) **for** b ˂0** reflects **f(x)** about **y-axis.**

**Hook Questions:**

*1. **What is meant by vertical stretch?*

*2. **What is horizontal compression?*

3. *What is meant by reflection of a function about x-axis?*

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