Which of the following statements is true about the graphs of f(x)=x and g(x)=f(x+7)?

Question

A. g(x) is the graph of f(x) translated 7 units down.

B g(x) and f(x) have the same y-intercept.

C g(x) is the graph of f(x) translated 7 units to the left.

D g(x) is the graph of f(x) translated 7 units to the right.

Answer 1

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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Answer 2

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.

Answer 3

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

Answer 4

Here is a picture. Always graph the function to get a Big Picture. A picture is worth 1000 words in geometry.