Answer to Question #257184 in Algebra for Charity

Question

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

Calculate the coordinates of the intercepts of f with axes

Sketch the graph of f

Answer 1

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

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

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

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

The graph of f is shown below: