How do you compare the graph of g(x) = x + 7 to the graph of f(x) = x?

1 Answer
Jan 4, 2018

As shown below...

Explanation:

For this problem we can first use our transformation knowledge, where if # y = f(x) # then # y = f(x) + c # just simply means a transformation of #(0, c) # or in other words, a shift upward by #c#

So hence #g(x) = x+7 # is simply the graph # y = f(x) # sheted 7 units upward...

We can also verify this by graphing the different lines, where we can tabualte a few values and draw the two lines...

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We can also see that the purple line, #g(x)# , is the black line, #f(x)#, shited 7 upward...

#=> g(x) = f(x) + 7 #

Hence the two lines are also parrallel as they have the same gradient, and they never intersect...