Victory for the ACT Student Text 15e

L ESSON 2 | A LGEBRA AND F UNCTIONS • 221 37. Which of the following is the complete solution set for x 2 1 3 > − ? A. All real numbers B. The null set C. All real numbers less than –1 or greater than 2 D. All real numbers less than –2 or greater than 1 E. All real numbers less than –3 38. If x 3 6 9 > − , then which of the following must be true? F. x 3 2 < < − G. x 2 3 < < − H. x 3 < − or x ! 2 J. x 1 or x 5 ! K. x 1 or x 9 ! 39. Š‹…Š ‘ˆ –Š‡ ˆ‘ŽŽ‘™‹‰ ‹†‡–‹ϐ‹‡• exactly those values of x that satisfy 4 < ? x 2 4 − + A. x ! 4 B. x 4 C. x 0 ! D. x 0 4 E. x 4 0 < < −

35. Which of the following is the complete solution set for x 3 2 1 5 + = ? A. { 8 , 7 } B. { , } 8 7 C. { , }7 7 36. Which of the following is the complete solution set for x x 6 3 + = ? F. ,3 2 3 ( 2 G. , 2 3 3 ( 2 H. , 2 3 3 ( 2 J. { }3 K. {} D. { }7 E. { }8

Equations Involving Absolute Value Items #35–36

Throwback to Math

Inequalities Involving Absolute Value Items #37–39 Class To solve equations involving absolute values, construct two derived equations and solve for x in each equation. Test the values for x in the original equation to verify that each is a valid solution.

Throwback to Math Class The key to solving inequalities involving absolute value is to recall the following properties of absolute value: If x a $ ( a 0 ! ), then x a # or x a $ . If x a # ( a 0 ! ), then x a # or x a & $ a x a # # . EVALUATING, INTERPRETING, AND CREATING ALGEBRAIC FUNCTIONS

, what is the value of

If ( ) ( ) f 2 ? F. 8 G. 2 H. 2 J. 8 K. 12 f x x x 2 = +

If ( ) y f x = = − − − e o for all integers and x 1, what is the value of y ? A. 2 B. 2 1 C. 4 1 D. 2 1 E. 2 x x 6 2 2 x 2 1

40.

Function Notation Items #40–47

41.

Throwback to Math Class Function notation is f ( x ), which means the output is a function of x .