Question

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

Answer 1

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...

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...