The general form of a member of the reciprocal function family is Identify the values of a, h, and k in the given function.
y= 5/x+6 −2
State the transformations on the graph as a result of a, h, and k.
The general form of a member of the reciprocal function family is y = a/(x - h) + k
Comparing this to y= 5/x+6 −2, we can see that:
a = 5
h = -6
k = -2
The transformation on the graph as a result of a, h, and k are as follows:
- a affects the shape of the graph, making it steeper or shallower.
- h affects the horizontal shift of the graph.
- k affects the vertical shift of the graph.
In this case, a = 5 implies that the reciprocal function will be relatively steep. h = -6 implies that the graph will shift 6 units to the right. k = -2 implies that the graph will shift 2 units down.
I suspect you want 5/(x+6) - 2 since you mentioned the reciprocal function (1/x)
So we have undergone
shift left by 6
stretch vertically by 5
shift down by 2
Apologies for the mistake in the initial expression. Yes, you are correct, it should be 5/(x+6) - 2 for a member of the reciprocal function family.
As a result, we have undergone the following transformations on the graph:
- Shift left by 6, since h = -6.
- Stretch vertically by 5, since a = 5.
- Shift down by 2, since k = -2.
Thank you for catching my mistake and providing the correct transformations.
To identify the values of a, h, and k in the reciprocal function, let's examine the given equation:
y = 5/(x + 6) - 2
The general form of a reciprocal function is:
y = a/(x - h) + k
Comparing this general form with the given equation, we can identify the values of a, h, and k in the following way:
a = 5, h = -6, k = -2
Now, let's discuss the transformations that occur on the graph due to these values:
1. Vertical Stretch/Compression (a):
The value of 'a' in the general form determines the vertical stretch or compression of the graph. In this case, since a = 5, there is no vertical stretch or compression occurring. The graph remains unchanged in this aspect.
2. Horizontal Translation (h):
The value of 'h' in the general form indicates the horizontal translation of the graph. In this case, h = -6, which means the graph is shifted 6 units to the left. The entire graph will be moved to the left by 6 units.
3. Vertical Translation (k):
The value of 'k' in the general form represents the vertical translation of the graph. In this case, k = -2, indicating that the graph is shifted 2 units downwards. The entire graph will be shifted downwards by 2 units.
To summarize, for the given function y = 5/(x + 6) - 2:
- There is no vertical stretch or compression.
- The graph is horizontally translated 6 units to the left.
- The graph is vertically translated 2 units downwards.