|
Question 1166141: how do you compare the function y=5(1/2)^x to the exponential parent function
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe, based on the reference i found at , that the parent function is y = b^x and that parent function can be transformed by the form of y = a * b^(x-h) + k.
a is the vertical transformation, b is the base, x is the exponent, h is the horizontal shift, k is the vertical shift.
the vertical transformation will either expand (a is > 1) or contract (a is less than 1) or reflect the the graph about the x-axis.
(x-h) will shift the graph to the left (h is positive) or to the right (h is negative).
k will shift the graph either up (k is positive) or down (k is negative).
your equation is y = 5 * (1/2) ^ x.
i believer the base function would be y = b^x where be = 1/2.
the graph of that function is shown below:
y = (1/2) ^ 0 crosses the y-axis at y = 1, since any base raised to the power of 0 will be equal to 1.
the function of y = 5 * (1/2) ^ x appears to be the same function that has been expanded because a is positive.
there is no horizontal shift (h = 0) and there is no vertical shift (k = 0).
the only change is that the value of y is 5 times greater than it would be with the base function for the same value of x.
in the following graph, the value of a = 5 expands the graph by 5 times what the value of y would be in the base graph.
at x = -1, the expanded graph y value is 10 rather than 2; at x = 0, the expanded y value is 5 rather than 1; at x = 2, the expanded graph y value is 1.25 rather than .25.
in each case, the expanded y value is 5 times the base y value because the value of a is 5 rather than 1.
1 is the default value of a.
if the value of a is not shown, it is same as if it is equal to 1.
here is the graph of the expanded function compared to the base function.
the base function is in red.
the expanded function is in blue.
here is an excellent reference on the subject.
https://mathbitsnotebook.com/Algebra2/Exponential/EXExpFunctions.html
the reference to other information concerning high school math subject from this site can be found at http://mathbitsnotebook.com/
|
|
|
| |
