Domain, range and graphs help pls?

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1 Answer
Jan 31, 2018

bottom-left graph
(see below for other answers)

Explanation:

the graph needed is on the bottom left.

this is visible from the circles on the graph.

if a circle at a certain point of the graph is blank (white), it means that that point is not part of the graph.

for #t^2#, where #0< t <3#,
the values #0# and #3# for #t# are not included, since it is a strong inequality.

this means that where #t = 0# and #t = 3#, the #xy#-coordinates will not be included. because of this, the points where these two values would be, if included, are blank circles instead.

the domain of the function is #0 < t <= 21.5#.

between these values, there are defined #y#-values for every value of #t# - there are no gaps between the definitions of the functions given.

this means that the inequality signs, after the smallest #t#-value and before the largest #t#-value, can be used to find the domain.

the range of the function is #0 <= y <= 33#.

this can be found from the largest and smallest #y#-values for the function #y = -2t + 43, 5 <= t <= 21.5#

#t = 5: y = 43 - 10 = 33#
#t >= 5: y <= 33#

#t = 21.5: y = 43 - 43 = 0#
#t <= 21.5: y >= 0#

#q(1) = 1^2 = 1#
#q(3) = 9 + 9 = 18#
#q(5) = 33#
#q(7) = 43 - 14 = 29#