EXPONENTIAL TRANSLATIONS

Exponential Translations

y = a b∙ x-h+k-h

h tells us how the function moves left or right (don’t forget that h is being subtracted!)

+k

k tells us how the function moves up or down

Example 1

Describe the translation:y = 2 4∙ x-6-5

h=

k=

Opens up or down?

Example 2

Describe the translation:y = -3 2∙ x+2+4

h=

k=

Opens up or down?

Example 3

How would the function y = 3 4∙ x be written if it was translated down 2 and right 7?

Example 4

How would the function y = 5 2∙ x be written if it was translated left 3 and up 9?

Exponential Regression

What if we are given a graph or data that looks like it has an exponential trend?

How do we find an equation for it?

Exponential Regression Steps

1. Enter the data into L1 and L2. (STAT → Edit…)2. Use the ExpReg tool. (STAT → CALC)3. Substitute the value for a and b into the

equation y = a(b)x.

Try it!The data at the right shows the

cooling temperatures of a freshly brewed cup of coffee after it is poured from the pot. The pot’s temperature is approximately 180° F. Find an exponential regression model for the data.

Time (mins) Temp ( ° F)

0 179.55 168.78 158.1

11 149.215 141.718 134.622 125.425 123.530 116.334 113.238 109.142 105.745 102.250 100.5