What is the transformation that occurs to the equation y=2^x if the equation changes to y= 2^x-3+4.

Question

anteater · Answer

Is your equation  y = 2^x - 3 + 4  or $$2^{x-3} + 4$$ ?

anteater · Answer

I am presuming it is the second one, which would shift the graph right 3 units and up 4.

mathmale · Answer

anteater is right in asking exactly what you meant by y=2^x-3+4.  Without parentheses, you have in effect written y=2^x+7.  I'm sure that's not the function you found in your homework assignment.

It is absolutely essential that you enclose that (x-3) in parentheses.  If you do that, you end up with $$y=2^{(x-3)}+4.$$

mathmale · Answer

this tells the reader that the exponent here is (x-3), and not just x.

mathmale · Answer

Now, if you begin with y = 2^x, and graph it, you'll find that the outcome is an exponential function whose y-intercept is 1.

If you (1) translate this graph 3 units to the right, (2) as well as 4 units up, you have in fact gone from y = 2^x to y = 2^(x-3) + 4.