Victory for the ACT Student Text 15e

L ESSON 2 | A LGEBRA AND F UNCTIONS • 223 54. The cost of making a call using a phone card is $0.15 for dialing and $0.04 per minute of connection time. Which of the ˆ‘ŽŽ‘™‹‰ ‡“—ƒ–‹‘•…‘—Ž† „‡ —•‡† –‘ ϐ‹† the cost, y , of a call x minutes long? F. ( . . ) y x 0 04 0 15 = + G. . . y x 0 04 0 15 = + H. . . y x 0 04 0 15 = + J. . . y x 0 15 0 04 = − K. . . y x 0 04 0 15 = −

53. At 9:00 a.m., when the heat is turned on, the temperature of a room is 55°F. If the room temperature increases by n °F each hour, which of the following expressions can be used to determine the number of hours needed to bring the temperature of the room to 70°F? A. ( ) ( ) n 55 70 B. ( ) ( ) n 55 70 C. ( ) n 70 55 D. ( ) n 70 55 E. ( ) n 55 70

Throwback to Math Class Expressions and functions can be used to formally describe relationships between real world factors like price and sales or number of students and number of required texts. Functions as Models items will challenge you to create an expression or equation that expresses these relationships. Note that a function is the same as any equation representing one variable as a function of another.

Throwback to Math Class The domain, or input of a function, is the set of all values for which –Š‡ ˆ—…–‹‘ ‹• †‡ϐ‹‡†Ǥ Š‡ ”ƒ‰‡ ‹• –Š‡ •‡– ‘ˆ ƒŽŽ ˜ƒŽ—‡• –Šƒ– ƒ”‡ –Š‡ result, or output, of the function for the values in the domain. Remember that the domain can be tricky when you’re dealing with rational or radical equations. Recall that for rational equations, values that make the denominator zero are not in the domain. For radical equations, values that make the radicand negative are not in the domain.

SOLVING SIMULTANEOUS EQUATIONS

If x y A. 0 B. 1 C. 2 D. 3 E. 4 4 + = If x y 2 8 + = F. –2 G. –1 H. 0 J. 1 K. 3 If x 7 2 A. 2 B. 3 C. 4 D. 5 E. 6

and y

– x

2, then x

?

If x y 2 8 + = value of x y ? F. –1 G. 1 H. 2 J. 3 K. 5 If x y 4 5 12 + = the value of ( ) x y 7 ? A. 7 B. 14 C. 49 D. 77 E. 91 and x y

, what is the

1 − =

55.

58.

and x

– y

1, then x

?

and x y 3 4 5 + =

, what is

56.

59.

and y x 3 7 10 − =

, then y

?

57.