Inverse Test

1. AIP-Test Inverses Name___________________________________
.
1) Which graph represents a function in a one to one correspondence?
A) B)
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
C) D)
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
2). For a function 푓(푥)could there be a point where     1 f x f x   ?
If so, what is a possible point where this occurs.
A) No, it is impossible you can never have     1 f x f x  
B) Yes it is possible, (2, 4)
C) Yes it is possible, (-5, -5)
D) Yes it is possible, (0, 2)
Restrict the domain to insure that the inverse is a function.
3)푓(푥) = 2푥 2 + 5 4) 푓(푥) = 1
4
푥 − 6
a) all real numbers a) all real numbers
b) all real numbers where x ≥ 5 b) all real numbers except when x ≠ -4
c) all real numbers where x ≥ 0 c) all real numbers except when x ≠ -6
d) all real numbers where x < 2 d) all real numbers except when x ≠ 6

2. 5) 6)
a) all real numbers a) all real numbers
b) all real numbers where x ≥ 1 b) all real numbers except when x > 6
c) all real numbers where x ≥ -2 c) all real numbers except when x < -8
d) all real numbers where x < -3 d) all real numbers except when x < -1
Determine whether f(x) is invertible.
7) 8)
a) Yes, because it fails the vertical line test a) Yes, because it fails the vertical line test
b) No, because it fails the horizontal line test b) No, because it passes the horizontal line test
c) Yes, because it fails the horizontal line test c) Yes, because it passes the horizontal line test
d) No, because it passes the vertical line test d) No, because it passes the vertical line test

3. Determine whether f(x) is a one to one function.
9) 10)
a) Yes, because it fails the horizontal line test a) Yes, because it fails the vertical line test
b) No, because it passes the vertical line test b) No, because it passes the horizontal line test
c) Yes, because it passes the vertical line test c) Yes, because it passes the horizontal line test
d) No, because it fails the horizontal line test d) No, because it passes the vertical line test
Which of these points is NOT a point on the graph of the inverse of f(x):
11) 푓(푥) = 3푥 − 5 12) 푓(푥) = 1
2
푥 2 − 5 , 푥 ≥ 0
a) (-2, 1) a) (-3, 2)
b) (-5, 0) b) (-4 ½ , 1)
c) (-1, 6) c) (3, 4)
d) (1, 2) d) (0, -5)

4. These two questions are NOT multiple choices.
Graph the inverse of the function. Graph carefully and accurately!
24) 25)