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:
f(x) = a/(x-h) + k
In the given function y = 5x+6-2, we can see that:
a = 5
h = 0 (since x is not being shifted horizontally)
k = 4 (since -2 is being added to the output or y value)
The transformations on the graph as a result of a, h, and k are as follows:
1. a > 0: The graph is vertically stretched by a factor of |a|.
Here, a = 5 > 0. So, the graph is vertically stretched by a factor of |5| = 5.
2. h > 0: The graph is shifted to the right by h units.
Here, h = 0. So, there is no horizontal shift.
3. k > 0: The graph is shifted upwards by k units.
Here, k = 4 > 0. So, the graph is shifted upwards by 4 units.
Overall, the graph is vertically stretched by a factor of 5 and shifted upwards by 4 units.