Question

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

Functions
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asked 2020-11-08
How do changes in parameters relate to translations of the graphs of exponential functions?

Answers (1)

2020-11-09

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.

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