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Graphing Square Root Functions, a la Shmoop. Teddy has been fascinated by dinosaurs for
years... ...which is why he's super excited that he
just got a pet stegosaurus for his birthday. However, the initial excitement is wearing
off and reality is setting in... he's going to have to take care of this thing.
Steven... that's the stegosaurus... is whining at the door, and clearly needs to be walked.
Teddy's worried about being able to keep up with his new, large friend.
Is there a way he can find out how fast Steven will walk?
As it just so happens, Teddy finds a "dinosaur speed" equation online. All he has to do now
is graph it. y equals the square root of t minus 3, where
t is time in seconds, and y is feet. To start, let's first check the domain of
the equation, or what t-values are possible that allow the function to work.
Since we know the inside of a square root function can't be negative...
...we can set the inside of the equation t-3 to be greater than or equal to 0.
By adding 3 to both sides, we see that the possible t's of the function are all greater
than 3. Now we can make a table of values.
We know the graph doesn't exist at any values of t less than 3...
...so we don't even need to bother trying points less than 3.
If we plug in t equals 3 to the y equation, we get the square root of 3 minus 3, which
equals 0. If t equals 4, the square root of 4 minus
3 is the square root of 1, which is just 1. If t equals 7, we get the square root of 7
minus 3, or the square root of 4, which is 2.
If t equals 12, the square root of 12 minus 3 is root 9, which equals 3.
Notice that we chose t-values that would give us nice, neat y-values....
Now let's plot these bad boys. (3,0), (4,1), (7,2), and (12,3)... and draw a smooth curve
through the points. Expect square root functions to be curved
lines, and don't try to graph a straight line through these points.
Now that Teddy has found that Steven can walk 3 feet in 12 seconds...
...he can rest assured that he's not going to be dragged all the way from his home to
the dinosaur park.