Question #257184

Consider the function of f(x)=4^-x -2


Calculate the coordinates of the intercepts of f with axes


Sketch the graph of f






1
Expert's answer
2021-10-27T13:46:09-0400

A y-intercept is a point where the graph of a function intersects the y-axis (x=0x=0):

f(0)=402=1f(0)=4^0-2=-1

An x-intercept is a point where the graph of a function intersects the x-axis (y=0y=0):

f(x)=04x=2x=log42=1/2x=1/2f(x)=0 \Leftrightarrow 4^{-x}=2 \Leftrightarrow -x=\log_4 2=1/2 \Leftrightarrow x=-1/2

The graph of f is shown below:


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