Victory for the ACT Student Text 15e

222 • M ATH

48. If ( ) 5 5 < < − , which of –Š‡ ˆ‘ŽŽ‘™‹‰ †‡ϐ‹‡• –Š‡ ”ƒ‰‡ ‘ˆ ( ) f x ? F. ( ) f x 17 13 < < − G. ( ) f x 13 17 < < − H. ( ) f x 5 12 < < − J. ( ) f x 0 17 K. ( ) f x 3 13 − + , for which of the following values of x is ( ) f x —†‡ϐ‹‡†ǫ A. –2 B. –1 C. x x 2 2 = − , which of the following †‡ϐ‹‡• –Š‡ ”ƒ‰‡ ‘ˆ ( ) f x ? F. All real numbers G. All real numbers except –2 H. All real numbers except 0 J. All real numbers except 2 K. All real numbers greater than 2 If x 4 8 12 < − , which of the following †‡ϐ‹‡• –Š‡ ’‘••‹„Ž‡ ˜ƒŽ—‡• ‘ˆ x ? A. x 8 4 < < − − B. x 4 8 < < − C. x 1 5 < < − D. x 1 5 E. x 4 8 52. In a certain game, a player picks an integer between 1 and 10, adds 3 to it, multiplies the sum by 2, and subtracts 5. If x is the number picked by a player, which of the following correctly expresses –Š‡ ϐ‹ƒŽ ”‡•—Ž– ‘ˆ –Š‡ ‰ƒ‡ǫ F. ( ) ( ) x 3 2 5 − + G. x 3 2 5 + − H. ( ) x 2 3 5 + − J. ( ) x 2 3 5 + − K. ( ) ( ) ( ) x 2 3 5 f x x 3 2 = − and x 49. If ( ) f x x x 1 2 = 2 1 D. 1 J. 2 If ( ) f x 50. 51.

If ( ) the value of ( ( )) f g 2 ? F. 2 G. 0 H. 2 J. 4 K. 10 the value of ( ( )) g f 2 ? A. 15 B. 12 C. 6 D. 3 E. 2 is the value of ( ) g 1 ? F. 3 G. 18 H. 21 J. 39 K. 55 f x x 3 = + and ( ) If ( ) f x x 3 2 = + and ( ) If ( ) f x x x 2 2 = +

, what is

g x x 2 5 = −

42.

The Cambridge Edge Item #42 requires you to evaluate one function for a given value and to use that result to evaluate a second function. This is also known as composing one function with another. Throwback to Math Class A function is an equation where each input has exactly one output. For example, x y 2 is NOT a function because the input x 1 corresponds to both y 1 and y –1. Graphically, a function will always pass the vertical line test (any vertical line will intersect a function at no more than one point). Concepts of Domain and Range Items #48–51 Functions as Models Items #52–54

, what is

g x x x 2 = +

43.

and ( ) ( ( )) g x f f x

, what

44.

and ( ) does ( ) ( ) f x g x ? g x x 2 1 = −

, for

If ( ) what value of x A. 5 B. 2 C. 0 D. 3 E. 7 If x x x 2 = − F. –6 G. –2 H. 0 J. 4 K. 6 If x x x 2 = − A. 27 B. 30 C. 58 D. 72 E. 121 f x x 3 4 = +

45.

for all integers, then ? 2 − =

46.

for all integers, then ? 3

47.