Answer:
Step-by-step explanation:
(f + g)(x) simply means that you are adding together the 2 functions that are written in terms of x.
The only like terms we have there are the x-cubed's, so
Pleaseeee help!!! I will mark you as brainlinest for correct answer!!!
1 answer:
Answer: choice C) g(x) = -2^(x+8)+3
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Explanation:
To go from f(x) to g(x), we need to do two transformations:
Transformation 1: shift 8 units to the left
Transformation 2: shift 3 units up
To pull off Transformation 1, we will replace every x with x+8. What this does is shift the entire xy axis 8 units to the right giving the illusion that the graph has moved 8 units to the left (when in reality the curve hasn't shifted at all). So that explains why we have x+8 there
Side Note: it is NOT x-8 because that will shift the graph to the right 8 units. So it is NOT choice A. This is a trap/trick answer.
Now onto Transformation 2. To do this, we effectively add 3 to both sides of the f(x) function. So f(x) = -2^x becomes f(x)+3 = -2^x + 3
Applying Transformation 1 and Transformation 2 at the same time has us go from f(x) = -2^x to f(x+8)+3 = -2^(x+8)+3, or in other words,
g(x) = -2^(x+8)+3 which is why choice C is the answer.
GeoGebra confirms the answer. See the attached image.
Side Note: it looks like f(x) touches or lays on the x axis, but this isn't the case. Instead, the function curve gets closer and closer to the x axis but never touches. There is a horizontal asymptote here. The same applies for g(x) as well but the horizontal asymptote is the line y = 3. It has been shifted up 3 units.
-------------------------------
Explanation:
To go from f(x) to g(x), we need to do two transformations:
Transformation 1: shift 8 units to the left
Transformation 2: shift 3 units up
To pull off Transformation 1, we will replace every x with x+8. What this does is shift the entire xy axis 8 units to the right giving the illusion that the graph has moved 8 units to the left (when in reality the curve hasn't shifted at all). So that explains why we have x+8 there
Side Note: it is NOT x-8 because that will shift the graph to the right 8 units. So it is NOT choice A. This is a trap/trick answer.
Now onto Transformation 2. To do this, we effectively add 3 to both sides of the f(x) function. So f(x) = -2^x becomes f(x)+3 = -2^x + 3
Applying Transformation 1 and Transformation 2 at the same time has us go from f(x) = -2^x to f(x+8)+3 = -2^(x+8)+3, or in other words,
g(x) = -2^(x+8)+3 which is why choice C is the answer.
GeoGebra confirms the answer. See the attached image.
Side Note: it looks like f(x) touches or lays on the x axis, but this isn't the case. Instead, the function curve gets closer and closer to the x axis but never touches. There is a horizontal asymptote here. The same applies for g(x) as well but the horizontal asymptote is the line y = 3. It has been shifted up 3 units.
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Correct Answer: - 550
We can use the distributive property to distribute the summation to the variables and then get the constant out to apply the summation formulas as shown below in the attached image.
The equation editor does not have a summation symbol, so I have attached the solution using the image.
The correct answer to this question is -550. First option is the correct one.
