A function f(x) undergoes the following transformations: vertical reflection, vertical stretch by a factor of 4, horizontal compression by a factor of 1/2, shift left 5, down 3. Use function notation to describe the transformed function:
g(x)=af(b(x-h))+k
Please help me! I'm confused!!!!!
vertical reflection: -f(x)
vertical stretch by a factor of 4: -4f(x)
horizontal compression by a factor of 1/2: -4f(2x)
shift left 5: -4f(2(x+5))
down 3: -4f(2(x+5))-3
Don't worry, I'm here to help you with a smile! π€‘
Let's break down the transformation step by step and fill in the values into the function notation:
1. Vertical reflection: Our a value will be -1, which reflects the graph vertically.
2. Vertical stretch by a factor of 4: The b value will be 4, indicating the vertical stretching.
3. Horizontal compression by a factor of 1/2: The h value will be 1/2 since it represents the horizontal compression. Just remember to flip it since it's a compression.
4. Shift left 5: The h value becomes h + 5, as it represents the horizontal shift.
5. Down 3: The k value will be -3, indicating a downward shift.
Putting it all together, the transformed function will be:
g(x) = -4f(2(x - 5)) - 3
I hope this clears up your confusion! Remember, math can be fun with a touch of humor. π
No worries! I'm here to help clarify the steps for you.
To describe the transformed function, let's break down the given transformations:
1. Vertical reflection: This means that the graph is flipped vertically. To achieve this, we need to multiply the function by -1.
2. Vertical stretch by a factor of 4: A vertical stretch stretches the graph vertically. To achieve a vertical stretch by a factor of 4, we need to multiply the function by 4.
3. Horizontal compression by a factor of 1/2: A compression squeezes the graph horizontally. To achieve a horizontal compression by a factor of 1/2, we need to multiply the x-values by 1/2.
4. Shift left 5: A left shift moves the graph to the left. To achieve a shift left 5 units, we need to add 5 to the x-values.
5. Shift down 3: A downward shift moves the graph down. To achieve a shift down 3 units, we need to subtract 3 from the function.
Putting it all together, the transformed function can be described as:
g(x) = 4 * (-1) * f((1/2)(x - 5)) - 3
It's important to note that the order of the transformations matters. In this case, we first reflected vertically, then stretched vertically, compressed horizontally, shifted left, and finally shifted down.
Sure! Let's break down the given transformations step by step:
1. Vertical reflection: This transformation reflects the graph of the original function vertically. In function notation, this is represented by -f(x).
2. Vertical stretch by a factor of 4: This transformation stretches the graph vertically by a factor of 4. In function notation, this is represented by 4*f(x).
3. Horizontal compression by a factor of 1/2: This transformation compresses the graph horizontally by a factor of 1/2. In function notation, this is represented by f(2x).
4. Shift left 5: This transformation shifts the graph 5 units to the left. In function notation, this is represented by f(2(x-5)).
5. Shift down 3: This transformation shifts the graph 3 units down. In function notation, this is represented by f(2(x-5))-3.
Putting it all together, the transformed function can be written as:
g(x) = -4*f(2(x-5))-3
Note that "a" represents the vertical reflection, "b" represents the horizontal compression, "h" represents the horizontal shift, and "k" represents the vertical shift. In this case, a = -4, b = 2, h = 5, and k = -3.