Chapter 1
To locate where
Y1 = Y2, press 2ND TRACE (CALC) 5
[intersect].
Press ENTER to mark the first curve. The cursor
jumps to the other function – here, the line. Next, press
ENTER to mark the second curve. Next, supply a guess for
the point of intersection. Use
◄ to move the cursor near the
intersection point you want to find – in this case, the leftmost
point. Press
ENTER . The break even point occurs when 10,050
gallons are sold and revenue is $22,110.
CHECKING YOUR ANSWER FOR A COMPOSITE FUNCTION We illustrate this
technique with the functions that are given on page 16 of Section 1.1 of Calculus Concepts:
altitude = F(t) =
−
2t
3
+ 1.8t
2
+ 1.7t + 4.4 thousand feet above sea level where t is the time into
flight in minutes and air temperature = A(F) = 279(0.85
F
) – 66 degrees Fahrenheit where F is
the number of thousand feet above sea level. Remember that when you enter functions in the
Y= list, you must use X as the input variable.
Press
Y= , and clear each previously entered equation with
CLEAR . Enter F in Y1 by pressing (−) . 2 X,T,θ,n ^ 3
+ 1 . 8 X,T,θ,n x
2
+ 1 . 7 X,T,θ,n + 4 . 4 ENTER
and enter A in Y2 by pressing 279 ( . 85 ^ X,T,θ,n ) − 66
ENTER .
Enter the composite function (A
o
F)(x) = A(F(x)) = Y2(Y1) in Y3
with the keystrokes
VARS ► 1 [Function] 2 [Y2] ( VARS
►
1 [Function] 1 [Y1] ) ENTER .
Next, enter your algebraic answer for the composite function in
Y4. Be certain that you enclose the exponent in Y4 (the func-
tion in
Y1) in parentheses.
(The composite function in the text is the one that appears to the
right, but you should enter the function that you have found for
the composite function.)
We now wish to check that the algebraic answer for the composite function is the same as the
calculator’s composite function by evaluating both functions at several different input values.
You can do these evaluations on the home screen, but as seen below, using the table is more
convenient.
TURNING FUNCTIONS OFF AND ON IN THE GRAPHING LIST Note in the prior
illustration that we are interested in the output values for only
Y3 and Y4. However, the table
will list values for all functions that are turned on. (A function is turned on when the equals
sign in its location in the graphing list is darkened.) We now wish to turn off
Y1 and Y2.
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16
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