Question

# How do changes in parameters relate to translations of the graphs of exponential functions?

Functions
How do changes in parameters relate to translations of the graphs of exponential functions?

An exponential function is of the form $$y=a(b)x−h+k$$.
h represents a horizontal translation since it affects the x-values. If h>0, the graph is translated to the right hh units. For example, $$y=3x−2$$ is the parent function of $$y=3x$$ translated 2 units to the right. If $$h<0h<0$$, the graph is translated to the left $$∣h∣$$ units. For example, $$y=3x+2y$$ is the parent function of $$y=3x$$ translated $$∣−2∣=2$$ units to the left.
k represents a vertical translation since it affects the yy-values. If $$k>0$$, the graph is translated up k units. For example, $$y=3x+2$$ is the parent function of $$y=3x$$ translated up 2 units. If $$k<0$$, the graph is translated down ∣k∣ units. For example, $$y=3x−2$$ is the parent function of $$y=3x$$ translated down $$∣−2∣=2$$ units.