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Functions (30 Problems)

1. Given functions f and g, perform the indicated operations.

f(x) = 7 - 7x, g(x) = -2x + 7
Find f + g.
A) -9x + 14
B) 5x
C) -2x + 7
D) -5x + 14
2. For the given functions f and g , find the indicated composition.

f(x) = 14x2 - 9x, g(x) = 12x - 8
(f g)(1)
A) 188
B) 52
C) 20
D) 136

3. Find the midpoint of the line segment whose end points are given.

(-1, 6) and (4, 9)
A) (3, 15)
B) (- , - )
C) ( , )
D) (-5, -3)

4. For the given functions f and g , find the indicated composition.

f(x) = 3x + 9, g(x) = 4x - 1
(f g)(x)
A) 12x + 35
B) 12x + 8
C) 12x + 12
D) 12x + 6

5. Write the standard form of the equation of the circle with the given center and radius.

(0, -8); 9
A) x2 + (y + 8)2 = 81
B) (x + 8)2 + y2 = 81
C) (x - 8)2 + y2 = 81
D) x2 + (y - 8)2 = 9

6. Begin by graphing the standard square root function f(x) = . Then use transformations of this graph to graph the given function.

g(x) = - 2

A)

B)

C)

D)

7. Begin by graphing the standard square root function f(x) = . Then use transformations of this graph to graph the given function.

g(x) = + 3

A)

B)

C)

D)

8. Find the midpoint of the line segment whose end points are given.

(3, 3) and (9, 6)
A) (12, 9)
B) (- 3, - )
C) (6, )
D) (-6, -3)

9. Find the distance between the pair of points.

(7, -5) and (3, -3)
A) 6
B) 2
C) 12
D) 12

10. Find the distance between the pair of points.

(7, 4) and (-7, -7)
A) 154
B)
C)
D) 3

11. Find the center and the radius of the circle.

(x - 5)2 + (y - 7)2 = 4
A) (-5, -7), r = 4
B) (-7, -5), r = 4
C) (5, 7), r = 2
D) (7, 5), r = 2

12. For the given functions f and g , find the indicated composition.

f(x) = , g(x) = 3x + 7
(g f)(x)
A) x
B) x + 14
C) 3x + 14
D) x -

13. Graph the equation.

(x - 2)2 + (y - 4)2 = 36

A)

Domain = (-4, 8), Range = (-2, 10)

B)

Domain = (-8, 4), Range = (-10, 2)

14. Given functions f and g, perform the indicated operations.

f(x) = 9x2 - 8x, g(x) = x2 - 3x - 40
Find .
A)
B)
C)
D)

15. Write the standard form of the equation of the circle with the given center and radius.

(-9, 8);
A) (x + 8)2 + (y - 9)2 = 4
B) (x - 9)2 + (y + 8)2 = 2
C) (x + 9)2 + (y - 8)2 = 2
D) (x - 8)2 + (y + 9)2 = 4
16. For the given functions f and g , find the indicated composition.

f(x) = 4x2 + 2x + 5, g(x) = 2x - 8
(g f)(x)
A) 8x2 + 4x + 2
B) 4x2 + 2x - 3
C) 8x2 + 4x + 18
D) 4x2 + 4x + 2

17. Find the distance between the pair of points.

(2 , -3) and (6 , 4)
A) 8
B) 9
C) 81
D)

18. Given functions f and g, determine the domain of f + g.

f(x) = 3x + 3, g(x) = 4x - 10
A) (-∞, 0) or (0, ∞)
B) (0, ∞)
C) (-∞, ∞)
D) (-∞, -3) or (-3, ∞)

19. Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the given function.

h(x) = (x + 3)2 + 7

A)

B)

C)

D)

20. Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the given function.

g(x) = x2 + 2

A)

B)

C)

D)

21. Determine which two functions are inverses of each other.

f(x) = x3 - 8 g(x) = h(x) = x3 + 8
A) f(x) and h(x)
B) g(x) and h(x)
C) f(x) and g(x)
D) None

2 2. Given functions f and g, determine the domain of f + g.

f(x) = 3x2 - 1, g(x) = 2x3 - 4
A) (-∞, -3) or (-3, -2) or (-2, ∞)
B) (-∞, 0) or (0, ∞)
C) (-∞, ∞)
D) (0, ∞)

23. Determine which two functions are inverses of each other.

f(x) = g(x) = 3x - 6 h(x) =
A) g(x) and h(x)
B) f(x) and g(x)
C) None
D) f(x) and h(x)

24. Complete the square and write the equation in standard form. Then give the center and radius of the circle.

x2 + y2 + 12x + 10y + 61 = 36
A) (x + 5)2 + (x + 6)2 = 36
(-5, -6), r = 6
B) (x + 6)2 + (x + 5)2 = 36
(-6, -5), r = 6
C) (x + 6)2 + (x + 5)2 = 36
(6, 5), r = 36
D) (x + 5)2 + (x + 6)2 = 36
(5, 6), r = 36

25. Does the graph represent a function that has an inverse function?

A) No
B) Yes

26. Write the standard form of the equation of the circle with the given center and radius.

(0, 3);
A) (x - 3)2 + y2 = 225
B) (x + 3)2 + y2 = 225
C) x2 + (y - 3)2 = 15
D) x2 + (y + 3)2 = 15

27. use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g.

g(x) = f(x) + 1

A)

B)

C)

D)

28. Given functions f and g, determine the domain of f + g.

f(x) = , g(x) =
A) (-∞, -10) or (-10, 5) or (5, ∞)
B) (-∞, -5) or (-5, -4) or (-4, ∞)
C) (-∞, -5) or (-5, 10) or (10, ∞)
D) (-∞, ∞)

29.Begin by graphing the standard function f(x) = x3 Then use transformations of this graph to graph the given function.

h(x) = (x + 2)3

A)

B)

C)

D)

30. Find the inverse of the one-to-one function.

f(x) = (x - 5)3
A) f-1(x) = - 5
B) f-1(x) = + 5
C) f-1(x) = + 125
D) f-1(x) = + 5

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