Answer:
options (a),(b) and (c) are correct.
Explanation:
(a)
" The two sides of a graph on either side of the axis of symmetry look like mirror images of each other " .
From the figure we could clearly see that the axis of symmetry of f(x) and g(x) is a vertical line passing through x=3.
Hence, the graphs share the same axis of symmetry.
option (a) is correct.
(b)
The y-intercept of a graph is a point where x=0.
we could clealy see from the figure that the y-intercept of the graph g(x) is '-5'
also when we will extend the curve f(x) on the positive y-axis we will observe that it will cut the y-axis at a positive number.
Hence, y-intercept of f(x) is greater than intercept of g(x).
option (b) is correct.
(c)
Clearly from the graph we could see that:
f(2)= -3
and g(4)=3
so the sum f(2)+g(4)= -3+3=0
option (c) is correct.
(d)
Domain is the region where the function is defined.
option (d) is incorrect as the both the graphs are extending so they take some value at every 'x' hence domain of both the functions are equal.
(e)
The graph of g(x) has a maximum '4' at x=3 but the graph of f(x) does not have a relative maximum as the graph is extending to infinity but it has a relative minimum '-5' at x=3.
option (e) is incorrect.