describe the transformations that produce the graph of g(x)=1/2(x-4)^3+5 from the graph of the parent function f(x)=x^3 give the order in which they must be preformed to obtain the correct graph
pls help!!!
Well, this sounds like a job for the Transformation Brigade! Here's the scoop:
First, we have the "inside the parentheses" transformation. It's all about the (x-4) term. This means we need to shift the graph 4 units to the right. So, picture the poor graph trying to move but it can't because of the parentheses. It's like trying to dance with a clown shoe on one foot!
Next up, the "raising to the power of 3" transformation. This is where things really get explosive! We take the graph and give it a power boost of 3. It's like pumping up a balloon till it bursts! This makes the graph steeper and more curvy, just like a roller coaster ride.
Lastly, the "outside the parentheses" transformation has its moment to shine! The (1/2) outside the parentheses is like a gentle breeze or a soft pillow. It squishes the graph vertically, making it shorter and fatter. It's like trying to squeeze into those jeans after eating too much cake!
So, in order to get the correct graph of g(x), you need to perform these transformations in this order: shift 4 units to the right, raise to the power of 3, and then squish vertically with a factor of 1/2. It's like transforming a plain potato into a fancy french fry!
I hope this helps and brings a smile to your face! If you have any more questions, just let me know!
To obtain the graph of the function g(x) = (1/2)(x-4)^3 + 5 from the graph of the parent function f(x) = x^3, several transformations need to be performed in a specific order. Here are the transformations in the correct order:
1. Horizontal shift: The graph of f(x) = x^3 is shifted 4 units to the right. This means you replace "x" with "(x-4)" in the equation, resulting in f(x + 4) = (x + 4)^3.
2. Vertical stretch: The graph is vertically compressed by a factor of 2. This is achieved by multiplying the equation by 1/2, giving f(x + 4) = (1/2)(x + 4)^3.
3. Vertical shift: The graph is shifted upward 5 units. Thus, you add 5 to the equation, resulting in g(x) = (1/2)(x + 4)^3 + 5.
So, when transforming the graph of the parent function f(x) = x^3 to the graph of g(x) = (1/2)(x-4)^3 + 5, you must perform the transformations in the following order:
1. Horizontal shift to the right by 4 units: f(x + 4)
2. Vertical compression by a factor of 2: (1/2)f(x + 4)
3. Vertical shift upward by 5 units: (1/2)f(x + 4) + 5, which simplifies to g(x) = (1/2)(x-4)^3 + 5.
To obtain the graph of g(x) = (1/2)(x - 4)^3 + 5 from the graph of the parent function f(x) = x^3, several transformations need to be performed in a specific order. Here's how you can do it step by step:
1. Horizontal Translation: Begin by applying a horizontal translation to the right of 4 units to the graph of f(x). This means shifting the entire graph horizontally by 4 units to the right.
2. Vertical Scaling: Next, perform a vertical scaling by a factor of 1/2 to the translated graph from step 1. This means each y-coordinate in the graph is multiplied by 1/2, making the graph steeper and closer to the x-axis.
3. Vertical Translation: Finally, apply a vertical translation of 5 units upward to the scaled graph from step 2. This means shifting the entire graph vertically by 5 units upward.
The correct order to perform these transformations is as follows:
1. Horizontal Translation
2. Vertical Scaling
3. Vertical Translation
Following this order will ensure that you obtain the correct graph of g(x) = (1/2)(x - 4)^3 + 5.
Hope this helps! Let me know if you have any further questions.
shift right 4: (x-4)^3
shrink vertically by a factor of 2: 1/2 (x-4)^3
shift up 5: 1/2 (x-4)^3 + 5
Better review your algebra 2 ...