Yes. (The graph is that of a function)
(a) A. Domain: ]-∞,∞[. Range: [-4,∞[
(b) A. The intercepts are (-5,0) , (-1,0) and (0,5)
Step-by-step explanation:
The vertical line test is a method to determine if a graph is a function by looking at its amount of intercepts with a random vertical. If there is more than one intercept with the random vertical line it isn't the graph of a function.
Here if you trace a random vertical line at any point of the graph you'll notice that it only intercepts it once. Hence it is a function's graph.
(a)
. The domain is given by the x-axis
On the graph, x can be any number: ]-∞,∞[
. The range is given by the y-axis
On the graph, y can be any number starting from -4 to higher : [-4,∞[
(b)
Intercepts are where the graph touches the x or y axis.
. The graph intercepts with the horizontal line (x-axis), at the point (-5,0) and (-1,0) : Notice y is = 0
. The graph intercepts with the vertical line (y-axis), at the point (0,5) : Notice x is = 0
NB:
When using intervals ∞ is always excluded. Because it is impossible to reach infinity,