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The parent function f(x)=2^x is reflected across the x-axis, then shifted 2 units left and 6 units down. Write an equation to represent the new function. 

 Jan 23, 2019
 #1
avatar+5172 
+2

\(\text{for any function }f(x) \\ \text{reflection across x-axis} \Rightarrow f(x) \to -f(x)\\ \text{left shift 2 units} \Rightarrow f(x) \to f(x+2)\\ \text{shift down 6 units} \Rightarrow f(x) \to f(x)-6\\ \text{combining all three}\\ f(x) \to -f(x+2)-6\)

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 Jan 23, 2019
 #2
avatar+2448 
+2

Thank you so much! ^-^

RainbowPanda  Jan 23, 2019
 #3
avatar+18274 
+2

Here is a graph FYI:

 

 Jan 23, 2019

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