Question

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.

Answer 1

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.

Answer 2

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

Answer 3

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.