For each exponential function, a) write a new function, and b) sketch the corresponding graph (on the same coordinate plane) bas
ed on the description of the transformation.
1 answer:
A reflection over the y-axis means that "x" will change signs.
A dilation causes the graph to stretch (if the factor is greater than 1) or shrink/compress (if the factor is between 0 and 1). Usually, the instructions will say whether it is a vertical or horizontal stretch (or shrink) so you know which variable is affected. Since it was not specified, I am going to assume that this is both a vertical and a horizontal shrink.
Answer: y = (
)
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For this case we have the following equations:
We must find
By definition of composition of functions we have to:
So:
We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.
So, the roots are:
The domain is given by all real numbers except 0 and 3.
Answer:
x other than 0 and 3