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## anonymous one year ago What statement correctly describes the key features of the graph of f(x) = −3(1/3)^x + 1 − 2?

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1. anonymous

Y-intercept of (0, −3), starts down on the left, gets closer to y = −2 on the right Y-intercept of (0, −3), starts up on the left, gets closer to y = −2 on the right Y-intercept of (0, 2), starts down on the left, gets closer to y = −1 on the right Y-intercept of (0, 2), starts up on the left, gets closer to y = −1 on the right

2. anonymous

@pooja195

3. IrishBoy123

and you say ... ?!?!

4. anonymous

A!

5. IrishBoy123

is it: $$\large f(x) = −3(\frac{1}{3})^{x + 1} − 2$$

6. anonymous

yes

7. IrishBoy123

$$f(x) = -3 (\frac{1}{3})^x . (\frac{1}{3}) -2 \\ = -(\frac{1}{3})^x -2$$ so $$f(0) = -3$$ and $$f(\infty) = -2$$ i'd have to agree with you

8. anonymous

@IrishBoy123 Would the graph start down on the left too?

9. anonymous

@ganeshie8

10. IrishBoy123

so, if you start with $$\large f(x)=−(\frac{1}{3})^x−2$$, then $$\large f(-100) = −(\frac{1}{3})^{-100}−2 \\ \large = −(\frac{3}{1})^{+100}−2 = −(3)^{+100}−2$$ ie a very large negative number.....

11. IrishBoy123

$$f(-1) = -(3)^1 - 2 = -5$$ play with the numbers

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