How do you find the range given #x=t^2-4# and #y=t/2# for #-2 <= t <= 3#?

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Answer 1 · 2017-12-21T19:11:11

Start with the inequality:

#-2 <= t <= 3#

Divide all 3 sections of the inequality by 2:

#-1 <= t/2 <= 3/2#

Use the parametric equation #y=t/2# to substitute y into the inequality:

#-1 <= y <= 3/2 color(red)(larr" this is the range")#

Here is a graph of the point #(t^2-4,t/2); -2 <= t <=3#

www.desmos.com/calculator

Please observe that the graph shows that the range is correct.