Question

Comparing graphs, please check my work.

Answer 1

Help me compare the graphs of \(y = \frac{1}{x}\) and \(y = \frac{5}{x+6}\).
I know that the general form of a reciprocal function is \(y = \frac{a}{x-h} + k\), where \(x \ne h\).

I know that:
a = Vertical stretch of the graph.
h = Horizontal translation.
k = Vertical translation.

Negative means the graph moves right, positive means the graph moves left.

So would it be correct if I said:
The graph has a vertical stretch by five, and a horizontal shift by six to the left.

Answer 2

Seems alright.

Answer 3

Thanks shamil, I have another question relating to this question though.
How does one graph \(y = \frac{1}{x}\)?
Do we make a table and plug in values?
That seems to work, but what happens if x = 0?
Is the graph simply undefined?

Answer 4

Sorry for the late reply, and yes it is discontinous when x = 0.
That's why there's a gap, between when x = 1 ,and x = -1.