00:01
Let's match this piece face function with its graph.
00:04
So here we have the definition of f -of -x, and that equals x -plus -4 if x less than or equal 0, and 2x plus 4 if x greater than 0.
00:14
So when we first observe these two pieces, they both have the same y -intercept.
00:20
That is 4 is the y -intercept in both cases.
00:24
So first, we can look out for the graph, which has the same intercept, y -intercept 4.
00:31
Of this six graphs which are given from a through e, a through f.
00:36
You see that only the graph in b as the y intercept for both pieces.
00:43
And also let's verify the other information.
00:47
So in the first part, if x less than or equal to zero, the slope of this function is one.
00:54
Clearly, we can see that for x less than or equal to zero, that is in this interval, the slope of this graph is rise over run and that is one so clearly it is one and also for x greater than zero that is in this interval the slope is two and it's also clear that the rise is two and then the run is one here so here the slope is two and thus it means both the conditions of this function which means this function corresponds to the graph in part b now let's match this function with its graph so here we have if of x equals x minus 4 if x less than or equal to 1 and this means the y intercept of this function is negative 4 of the graphs except to be only the graph in e has y intercept negative 4 this one is negative 4 other graphs do not have y intercept negative 4 so we can decide that this could be the graph of this function let's also determine the slope the slope of this one is positive 1 so this is clearly this is rise overrun which is 1 by 1 and that is 1 so this could be the graph of this function if we look at the other piece of this is 3x for x greater than 1 so when x x is greater than 1.
02:35
This is approximately there is rise over run and this looks like it is 3 by 1 and then the slope is 3.
02:45
So the graph of this function matches with the graph given in choice e...