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×You can see that what's being manipulated is the X value only, so you know it's horizontal (left to right) change, the equation for a horizontal change (x-k), so in the equation given it's (x-(-7), so the change is 7 to the left. The correct answer is C.
Feel free to message me if you need more help, I will reply ASAP!
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Patrick L. answered • 12/04/20
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f(x) = x
g(x) = f(x + 7) = x + 7
What I did is substitute x + 7 for the original x in the original function to get the transformed function.
In this case, the new function is shifted 7 units up from the original. However, since that is one of the choices we can say it is 7 units to the left because x - (-7) based on the general formula y = (x - h) + k.
Choice C is the correct answer.
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Raymond B. answered • 12/03/20
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f(x)=x is the same as y=x, a 45 degree upward sloping line through the origin, with slope =1 going through the origin
g(x)=f(x+7) is the same as y=x+7, a parallel line but shifted up by 7, the new y intercept.
shifting up by 7 is not one of the answers.
but shifting up by 7 is the same as shifting left by 7, since it is a 45 degree angle with slope = +1
Answer C is correct, although it misleadingly suggests it must be a shift to the left, when it is also a shift upward by 7
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Mostafa D. Report 12/04/20
Raymond B.
Just graph y=x and y=x+7. the y intercept is 7 higher, showing a shift up by 7. But because it has a slope of 1, it's identical to a shift to the left by 7. Plot a few points, graph them, and you can see they are equivalent, and that's true when the slope = 1Report
12/04/20
Mostafa D.
I understand, but in the problem it's f(x+7), the 7 is not being added to the whole equation, just to the X, so it would only be a horizontal change.Report
12/04/20
Raymond B.
they're equivalent, a leftward shift of a straight line with any finite nonzero slope is the same as an upward shift. They're equivalent. A leftward shift of y=x by 7 is the same as an upward shift of 7. y=x+7 is equivalent to y-7=x. You can call it manipulating x or manipulating y. But you go with the flow of whatever your instructor or textbook wants. You don't want to confuse some instructors. Although some might be impressed by your observation.Report
12/05/20
Zen F. answered • 12/03/20
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Here is a picture. Always graph the function to get a Big Picture. A picture is worth 1000 words in geometry.