Investigation 8 1 Consider the function f(x) = 2x+4. a Explain why fhas an inverse function f-1. b Complete the table for fand f-1. (x, f(x)) lies on the graph of f YL→X= f'v) v.fv) lies on the graph of f-1 y=f(x) xL»y = f(x) -4 A(-4,_) A'(-,-4) -2 B(_,-2) B'(-2,-) C(-,0) C'(0,-) D(0,_) D'(_,0) E(1, 6) 6 →1 E'(6, 1) 6. F(3,_) F'(-,3) c The points E and E' have already been plotted on the given set of axes. i Draw the graph of f(x) = 2x+4. 10 Also, clearly plot and label the other five points on the graph of fthat were found in part b. 6 ii Plot and label the other five points on the graph of f-1 that were found in part b. 4 2 d What can you say about the type of graph f-1 is? How would you find more points on this graph? Write down at least three more points on the graph -10 -8 of f-1, then complete the graph of f-. e What can you say about the position of the point B'with respect to the position of the point B? And what about the position of C' with respect to C? f There is one point that lies on both graphs. What is it? What do you notice about the coordinates of this point? -6 -4 -2 -2 2 4 8 10 -6 -8 -10 This point also lies on the line that bisects the first and third quadrants, the identity line. What is the equation of this line? Draw it with a dotted line on the set of axes. How would you describe the positions of the graphs of fand f-l with respect to the identity line? g Now explain how you would draw the graph of f1 if you are given the graph of f. h What is the equation of the inverse functionf-1? 4. 1. 3.
Investigation 8 1 Consider the function f(x) = 2x+4. a Explain why fhas an inverse function f-1. b Complete the table for fand f-1. (x, f(x)) lies on the graph of f YL→X= f'v) v.fv) lies on the graph of f-1 y=f(x) xL»y = f(x) -4 A(-4,_) A'(-,-4) -2 B(_,-2) B'(-2,-) C(-,0) C'(0,-) D(0,_) D'(_,0) E(1, 6) 6 →1 E'(6, 1) 6. F(3,_) F'(-,3) c The points E and E' have already been plotted on the given set of axes. i Draw the graph of f(x) = 2x+4. 10 Also, clearly plot and label the other five points on the graph of fthat were found in part b. 6 ii Plot and label the other five points on the graph of f-1 that were found in part b. 4 2 d What can you say about the type of graph f-1 is? How would you find more points on this graph? Write down at least three more points on the graph -10 -8 of f-1, then complete the graph of f-. e What can you say about the position of the point B'with respect to the position of the point B? And what about the position of C' with respect to C? f There is one point that lies on both graphs. What is it? What do you notice about the coordinates of this point? -6 -4 -2 -2 2 4 8 10 -6 -8 -10 This point also lies on the line that bisects the first and third quadrants, the identity line. What is the equation of this line? Draw it with a dotted line on the set of axes. How would you describe the positions of the graphs of fand f-l with respect to the identity line? g Now explain how you would draw the graph of f1 if you are given the graph of f. h What is the equation of the inverse functionf-1? 4. 1. 3.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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please do 1d 1h
Transcribed Image Text:Investigation 8
1 Consider the function f(x) = 2x+4.
a Explain why fhas an inverse functionf-1.
b Complete the table for fand f-1.
y=f(x) x →y = f(x) (x, f(x)) lies on
the graph of f
(y.f-(v)) lies on
the graph of f-1
A'(-,-4)
yLx = f'v)
-4
A(-4,_)
-2
B(_,-2)
B'(-2,-)
C(_,0)
D(0,-)
C'(0,_)
D'(_,0)
1
6
E(1, 6)
E'(6, 1)
F(3,_)
F'(-,3)
The points E and E' have already been plotted
on the given set of axes.
i Draw the graph of f(x) = 2x+4.
y
10 -
Also, clearly plot and label the other five points
on the graph of fthat were found in part b.
ii Plot and label the other five points on the graph
of f-1 that were found in part b.
E
4
2
d What can you say about the type of graph f-l is?
How would you find more points on this graph?
Write down at least three more points on the graph -10 -8
of f-1, then complete the graph of f-1.
e What can you say about the position of the point
B'with respect to the position of the point B? And
what about the position of C' with respect to C?
f There is one point that lies on both graphs. What is
it? What do you notice about the coordinates of
this point?
X
-2
-2
-6
-4
2
4
6
8.
10
-4
-6
-8
10
This point also lies on the line that bisects the first and third quadrants, the identity line. What is
the equation of this line? Draw it with a dotted line on the set of axes. How would you describe the
positions of the graphs of fand f-l with respect to the identity line?
g Now explain how you would draw the graph of f-1
if you are given the graph of f.
h What is the equation of the inverse functionf-1?
4
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