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

Jan 4, 2018

As shown below...

#### Explanation:

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

So hence $g \left(x\right) = x + 7$ is simply the graph $y = f \left(x\right)$ 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, $g \left(x\right)$ , is the black line, $f \left(x\right)$, shited 7 upward...

$\implies g \left(x\right) = f \left(x\right) + 7$

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