SOLUTION: find the relation to its parent graph for this: y=-(2)^x+5 -1

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Question 1158030: find the relation to its parent graph for this: y=-(2)^x+5 -1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

find the relation to its parent graph for this: y=-%282%29%5E%28x%2B5%29+-1
f%28x%29+=+a%2Ae%5E%28b%28x-c%29%29+%2B+d

c - Translate Graph Horizontally
When you subtract a positive number c from x, you are translating horizontally the graph of the function c units to+the right.
When c+is negative, you are translating horizontally the graph of the function c units to+the+left.

b - Horizontal Stretching+or Compression
When you multiply x by a positive b you will be performing either a horizontal compression or horizontal stretching of the graph.
If 0+%3C+b+%3C+1 you have a horizontal compression and if b+%3E+1 then you have a horizontal stretching.
When b is negative, then this horizontal compression or horizontal stretching of the graph is followed by a reflection across the y-axis.
a - Vertical Stretching or Compression
When you multiply a function by a positive a you will be performing either a vertical compression or vertical stretching of the graph.
If 0+%3C+a+%3C+1 you have a vertical compression and if a+%3E+1 then you have a vertical stretching.
When a is negative, then this vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.

d - Translate Graph+Vertically
When you add a positive number d+to a function, you are translating vertically the graph of the function d units upwards.
When d is negative, you are translating vertically the graph of the function d units downwards.

y=-%282%29%5E%28x%2B5%29+-1 compared to f%28x%29+=+a%2Ae%5E%28b%28x-c%29%29+%2B+d
a=-1=>a is negative, then this vertical+compression or vertical stretching of the graph is followed by a reflection across the x-axis
b=1=> there is no a horizontal compression or horizontal stretching
c=-5=>c is negative, you are translating horizontally the graph of the function 5 units to the left
d=-1=>d is negative, you are translating vertically the graph of the function 1 units downwards


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%282%29%5E%28x%2B5%29+-1%2C2%5Ex+%29+