SOLUTION: Please help! The graph of function h is created by shifting the graph of y=2^x to the left 3 units, then reflecting it in the x-axis, and finally shifting it up 8 units. Find h(x)

Algebra ->  Functions -> SOLUTION: Please help! The graph of function h is created by shifting the graph of y=2^x to the left 3 units, then reflecting it in the x-axis, and finally shifting it up 8 units. Find h(x)      Log On


   

Question 933404: Please help!
The graph of function h is created by shifting the graph of y=2^x to the left 3 units, then reflecting it in the x-axis, and finally shifting it up 8 units. Find h(x)
I think it's something on the order of: 2(x+3)+8 not sure about the 2. Unsure how to solve
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
When we have an exponential equation of the form y=a^x ± k, then the graph will be moved up or down k units.

When we make a change in the exponent of the equation, a left or right shift happens. In general, for an exponential equation of the form y=a^(x±c) the graph of y=a%5Ex will be moved left c units if c is positive, and right c units if c is negative.
If a negative sign is placed in front of an exponential function, then it will be reflected over the x-axis.
The graph of y+=+-a%5Ex can be obtained by reflecting the graph of y+=+a%5Ex in the x-axis.
The graph of the exponential equation y+=+a%5E%28-x%29 can be obtained by reflecting the graph of y+=+a%5Ex in the y-axis%7D%7D.%0D%0A%0D%0A%0D%0A%0D%0Ato+translated+left+%7B%7B%7B3 units means subtract 3
y=2%5E%28x-3%29

to reflect about the x-axis place a negative sign in front
y=-2%5E%28x-3%29
to shifting it up 8 units means add 8
y=-2%5E%28x-3%29%2B8
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C2%5Ex%2C+-2%5E%28x%2B3%29%2B8%29+