Answer:
So the equation is y = 3^(x + 4) - 2
Step-by-step explanation:
The first thing you should notice is that the graph almost hits y = -2 when x is going more and more negative. Only C and D can be correct. A and B both would move the graph to y = 2, some 4 units away (and up).
So now you have to distinguish between C and D. The easiest way to do this is to find the x intercept ( a point where y = 0)
0 = 3^(x+/-4) - 2 Add 2 to both sides
2 = 3^(x +/-4)
log(2) = log3^(x+/-4) Substitute the values for log2 and log3
0.3010 = (x +/- 4) 0.4771 Divide both sides by 0.4771
0.3010/0.4771 = x +/-4) Do the division
0.6309 = x +/- 4 The graph shows an intercept at around 3 (a little more then). There fore the equation must be
0.6303 = x + 4 Subtract 4 from both sides.
- 3.369 = x Answer
So the equation is y = 3^(x + 4) - 2
