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Graph the function below and state the domain and range. y = 1/5 e^-x - 5 We sta

ID: 2894598 • Letter: G

Question

Graph the function below and state the domain and range. y = 1/5 e^-x - 5 We start with the graph y = e^x from (a) and reflect about the axis to get the graph of y = e^-x in (b). (Notice that the graph crosses the y-axis with a slope of -1.) Then we compress the graph vertically by a factor of to obtain the graph of y = in (c). Finally we shift the graph units to get the desired graph in (d). The domain is R and the range is the interval .(a) y = e^x (b) y = e^-x (c) y = 1/5 e^-x (d) y = 1/5 e^-x - 5

Explanation / Answer

Then we compress graph vertically by factor of 1/5 to obtain graph of y = 1/5*e-x.

Range of function : The set of values of the dependent variable for which a function is defined

f(x) = 1/5*e-x - 5

Finding the inverse of function:

x = f(y)

x = 1/5*e-y - 5

- ln 5*(x + 5) = y = f-1(x)

FInding the domain of inverse function which will be range of f(x)

Domain of f-1(x) is : x + 5 > 0

x > -5

Range of f(x) Interval notation: (-5 , infinite)