Explanation:
the domain of a function is the interval or set of all valid x-values.
the range of a function is the interval or set of all valid y- values (= functional result values).
the intercepts are the points where the function intersects the coordinate axes.
remember, the functional value (y-value) to a given argument (x-value) is calculated by replacing any appearance of x in the function expression by the given argument, and then we do the basic calculation. that result is the functional value (y-value).
a.
what x-values are used ?
we see the curve going from x = 0 all the way to the right. the arrow indicates infinity (going on for all eternity).
the filled dot on the left end tells us that the point is included (an empty dot would say the point is excluded).
remember, included interval ends are indicated by "[", "]" symbols, excluded interval ends by "(", ")".
the domain is
[0 .. infinity)
"infinity" is not a number, only a concept, and therefore it cannot be included.
b.
what y-values do we see are used ?
it starts on the left side with 9, and then it goes up and up the further to the right we go. we don't see any indication of a limit, so also the y- values go finally to infinity.
the range is
[9 .. infinity)
c.
x-intercept - hmmm. is the curve intercepting the x-axis anywhere ? no.
so, B, there is no x-intercept.
d.
where did the curve intercept the y-axis ? exactly at y = 9 (and x = 0).
A. the y-intercept is 9.
e.
f(18) means what is the y-value of the point on the curve for x = 18 ?
your picture is a bit blurry, so I cannot see it clearly.
but it looks like the y-value at x = 18 is a little bit higher than y = 13.
it looks like y = 13.25