Given y=2^x
Predict the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.
I have:
y= -5 (2) ^ (x-2) - 5
Is this correct?
correct
Thank you!
actually that's wrong..
that will give you a reflection in the x-axis if you want a reflection in the y-axis you have to make the x in the exponent negitive.
i believe the answer is
y=5*2^((-x)-2)-5
To reflect the graph in the y-axis, we need to replace x with -x.
Thus, the new equation becomes y = 2^(-x).
To vertically stretch the graph by a factor of 5, we replace y with 5y.
The equation now becomes 5y = 2^(-x).
To translate the graph 2 units to the right, we need to replace x with (x - 2).
The equation now becomes 5y = 2^(-(x - 2)).
Finally, to translate the graph 5 units down, we subtract 5 from both sides of the equation.
The final equation is therefore 5y - 5 = 2^(-(x - 2)).
So, your equation y = -5(2^(x - 2)) - 5 is incorrect.
The correct equation is 5y - 5 = 2^(-(x - 2)).