+0

Parent function

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279
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+2448

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
+6099
+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
+2448
+2

Thank you so much! ^-^

RainbowPanda  Jan 23, 2019
#3
+20239
+1

Here is a graph FYI:

Jan 23, 2019