Question

I'm in dire need of help!!! 1) The red graph (1) is the graph of f(x) = 2x. Describe the transformation of the blue function (2) and write the equation of the graph.

Answer 1

Starting with the red graph, to arrive at the blue graph do the following transformations:
1) Reflect the red graph about the x-axis
2) Translate the graph up by 3 units along the y-axis.

Answer 2

I don't know how to do that though, which why i need some more explaining. I'm home schooled.

Answer 3

To reflect a graph about the x axis, stick a negative sign before the function.
Here, the red graph is \(y = 2^x\).
To reflect it about the x-axis, put a negative sign in front of the function:
\(y = -(2)^x\).
To move it up by 3 units, add 3 to he function:
\(y = -(2)^x + 3\).

Answer 4

You may want to check your usage of "dire" here! You may be in dire need of help, but not dire help :-)

Answer 5

Ahh sorry, I fixed it.

Answer 6

There may be a small translation along the x axis too but it is hard to read from the graph.

Answer 7

Perhaps not. Both pass through y = 1 when x = 0 but the top end of the red graph is slightly to the right of bottom end of the blue graph when it should not be.

Answer 8

Are there answer choices?

Answer 9

No it just says that, I have to write the transformation of the blue function and the equation of the graph.

Answer 10

Then it has been answered already.
Transformation is: Reflection about the x-axis, followed by translation of 3 units along positive y-axis.
The equation of the blue graph is: \(y = -(2)^x + 3\)