Can someone help me with this question? I got the transformation for horizontal shift and vertical shift, however, I don't know how to find the vertical/horizontal compression/stretch.
1. Describe the transformations that were applied to the parent function to create the graph shown below. Then write the equation of the transformed function.
Parent function y=x^4
Here is the link to graph:
imgur dot com/Gkaln
I looked your graph and the new vertex is (-1,4)
so y = x^4 must have been translated to
y = (x+1)^4 + 4
but there could also be a compression , so let the new curve be
y = a(x+1)^4 + 4
from the graph we can see that (0,1) lies on the new curve
1 = a(1^4) + 4
-3 - a
so we have y = -3(x+1)^4 + 4
test for the other point shown
let x = -2
y = -3(-1)^4 + 4
= 1
all looks good
8th line should have said
-3 = a
(but you probably guessed that was a typo)
So it is a vertical stretch by -3?
How did you find out what a is if you knew it was UP 4, left 1?
Yes, the maginitude of the stretch is 3,
the - tells me the curve is opening downwards
I knew since the vertex was (-1,4)
and the parent graph of y = x^4 has a vertex at (0,0)
the graph must have moved 1 unit to the left and 4 units up
so we would get
y-4 = (x+1)^4
moving the -4 to the right made it +4
but y = (x+1)^4 + 4
would not pass through (0,1) as your picture shows.
so there must have been a stretch/compression.
that would be caused by some number in front of
(x+1)^4
so that is why I chose y = a(x+1)^4 + 4
subbing in the point (0,1) gave me a value of
a = -3
To determine the vertical and horizontal compression/stretch, we need to analyze the graph you provided. However, as an AI text-based bot, I cannot directly view or access images or external links. But don't worry, I can still guide you through the process of finding the vertical and horizontal compression/stretch without seeing the graph.
To identify the transformations without the graph, we can rely on the given equation of the transformed function and its relationship to the parent function. In this case, the parent function is y = x^4.
1. Vertical Compression/Stretch:
To determine the vertical compression/stretch, we need to check if the graph appears vertically stretched or compressed compared to the parent function. This is dependent on the coefficient of x in the equation of the transformed function.
If the coefficient of x is greater than 1 (e.g., y = ax^4, where a > 1), the graph is vertically compressed.
If the coefficient of x is between 0 and 1 (e.g., y = ax^4, where 0 < a < 1), the graph is vertically stretched.
If the coefficient of x is equal to 1 (e.g., y = x^4), there is no vertical compression or stretch.
2. Horizontal Compression/Stretch:
To determine the horizontal compression/stretch, we need to examine whether the graph appears horizontally stretched or compressed compared to the parent function. This is evident from the exponent of x in the equation of the transformed function.
If the exponent of x is greater than 1 (e.g., y = x^4+n, where n > 1), the graph is horizontally compressed.
If the exponent of x is between 0 and 1 (e.g., y = x^4+n, where 0 < n < 1), the graph is horizontally stretched.
If the exponent of x is equal to 1 (e.g., y = x), there is no horizontal compression or stretch.
By analyzing the given equation of the transformed function, you can determine whether the graph is vertically or horizontally compressed/stretched and by how much. Remember that the equation may have different variables or numbers rather than what I used for illustration purposes (a, n, etc.). Please refer to the actual equation given to identify the transformations and write the equation of the transformed function accordingly.