Question

Can someone help me with dilations of exponential functions?

Answer 1

I'm supposed to change this equation y = (1/4)^x so that there will be a reflection on the x-axis and a dilation of 2. This was my answer: y = 2 * (-1/4)^x

But when I used this calculator here: https://www.desmos.com/calculator
to graph the function, nothing came up. What did I do wrong?

Answer 2

@jim_thompson5910 @Nnesha

Answer 3

I don't think you can raise a negative number to a non-integer power.
dilation: (x,y) \(\rightarrow\) (kx,ky) where k is the dilation factor.
reflection about x-axis: (x,y)\(\rightarrow\) (x,-y)
I think you have put the negative sign in the wrong place.

Answer 4

So, where should it be then?

Answer 5

Dilation should be about the origin, since no centre of dilation is specified.
so (x,y)\(\rightarrow\)(2x,2y) since the dilation factor is two.
This means that when you plot, the picture should be double in size.

Answer 6

ok, your question says reflection first and then dilation.
It doesn't matter in this case, but it is better to follow the order because they don't always give identical results.

I gave the rule for reflection about the x-axis. Can you find the reflection function?

Answer 7

*reflected function

Answer 8

---------------------------------------------
Example:
y=x^2
(x,y)=(x,-y)
so
after reflection
y=-x^2
---------------------------------------------

Answer 9

@quickstudent ?

Answer 10

Shouldn't it be y = (-1/4)^x

Answer 11

You want the y to be negative, not the base of the exponential expression.
In the \(example\), the negative sign was outside of x, not within (-x)^2 is wrong, because it will always be positive, so no reflection.