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

Haven

Haven

Answered question

2020-11-08

How can modifications to the parameters affect how the graphs of exponential functions are translated?

Answer & Explanation

liannemdh

liannemdh

Skilled2020-11-09Added 106 answers

A function with an exponential shape is  y=a(b)xh+k.
h represents a horizontal translation since it affects the x-values. Graph translation to the appropriate hh units occurs if h>0. For example, y=3x2 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.
Given that it changes the yy-values, k represents a vertical translation. 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=3x2 is the parent function of y=3x translated down 2∣=2 units.

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