Question

Which graph represents f(x) =|x − 5| + |x − 4|?

Answer 1

The correct graph is graph 4. 

You can find this by looking for recognizable points. This is the easiest way to find composite graphs. In the graph f(x) =|x − 5| + |x − 4| both 5 and 4 yield the answer of 1. You can see that in the examples below:

f(x) =|x − 5| + |x − 4|
f(5) =|5 − 5| + |5 − 4|
f(5) =|0| + |1|
f(5) = 0 + 1
f(5) = 1

f(x) =|x − 5| + |x − 4|
f(4) =|4 − 5| + |4 − 4|
f(4) =|-1| + |0|
f(4) = 1 + 0
f(4) = 1

Now we can look for graphs that have those two reference points. The 4th graph is the only one that has those. 

Answer 2

Its definitely not graph c