When looking at graphs, which of the following statements is true about functions?

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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.

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When looking at graphs, which of the following statements is true about functions?

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.

What do you mean it's also a shift upward by 7?

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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 = 1

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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.

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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.

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12/05/20

When looking at graphs, which of the following statements is true about functions?

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.

How do you know if a graph describes a function?

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

Which of the following that can test a graph that is function?

Definition: VERTICAL LINE TEST If a vertical line drawn anywhere on the graph of a relation only intersects the graph at one point, then that graph represents a function. If a vertical line can intersect the graph at two or more points, then the graph does not represent a function.

Which graph represents a function answer?

To check whether the graph represents a function or not, we perform vertical line test. Vertical Line test: If any vertical line intersects a graph at exactly one point then the graph represents a function otherwise not. Looking into the graphs, the vertical line intersects the graph D at only one point.