Victory for the ACT Student Text 15e

M ATH Q UIZZES • 263

EXPLANATIONS

2

9

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b b &

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3

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Set { , , } A 2 1 0 = − − { , , B 1 0 1} = − . If a and b pairs ( , ) a b both set A and set B ? Ǥ Ͳ B. 2 C. 5 D. 6 E. 7

, and set is an element of set A a member of ǡ ˆ‘” Š‘™ ƒ›

&

.

1 0

0 0

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3

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13.

is an element of set B is the product ab

13. (D) Mathematics/Statistics and Probability/Sets ‹•– ƒŽŽ ‘ˆ –Š‡ ’‘••‹„Ž‡ ’ƒ‹”‹‰• ˆ‘” ( , ) a b ƒ†…Š‡… ‡ƒ…Š ’”‘†—…–ǡ ab , for membership in both sets A and B : (–2,–1): 2 1 2 : − − = (neither set) (–2,0): 2 0 0 : − = (both sets) (–2,1): 2 1 2 : − = − (set A ‘Ž›Ȍ (–1,–1): 1 1 1 : − − = (set B ‘Ž›Ȍ (–1,0): 1 0 0 : − = (both sets) (–1,1): 1 1 1 : − = − (both sets) (0,–1): 0 1 0 : − = (both sets) (0,0): 0 0 0 : (both sets) (0,1): 0 1 0 : (both sets) Therefore, 6 possible combinations of a and b return a product that is a member of both sets. 14. (F) Mathematics/Algebra and Functions/ Solving Algebraic Equations or Inequalities with One Variable/Equations Involving Absolute Value Solve the derived equations for x : x 2 4 + = & & x x 12 2 8 4 , and ( ) x 2 4 − + = & x x 12 2 16 8 & − = = − Ǥ Š‡… x 4 and x 8 = − ‹ –Š‡ ‘”‹‰‹ƒŽ ‡“—ƒ–‹‘ǣ ( ) 2 4 4 12 and + = ( ) 2 8 4 − + = . 12 12 − = Therefore, the complete solution set is { , } 8 4 . 15. (A) Mathematics/Algebra and Functions/ Evaluating, Interpreting, and Creating Algebraic Functions/Concepts of Domain and Range ‹˜‹•‹‘ „› œ‡”‘ ‹• —†‡ϐ‹‡†ǡ •‘ ( ) f x is —†‡ϐ‹‡† ˆ‘” ƒ› ˜ƒŽ—‡ ‘ˆ x that results in a zero in the denominator of the rational expression. Set the denominator equal to zero and solve for x : & x x 2 0 2 − − = = − . Therefore, ( ) f x ‹• —†‡ϐ‹‡† ˆ‘” x 2.

Throwback to Math Class •‡– ‹• ƒ…‘ŽŽ‡…–‹‘ ‘ˆ –Š‹‰•ǡ ’‡‘’Ž‡ǡ numbers, or even concepts. ”ƒ…‡–• ƒ”‡ —•‡† to indicate set membership.

Š‹…Š ‘ˆ –Š‡ ˆ‘ŽŽ‘™‹‰ ‹• –Š‡…‘’Ž‡–‡ solution set for x 2 4 12 + = ?

14.

F. { , } 8 4 G. { , } 4 8 H. { , } 0 8 J. { , } 4 8 K. { ,6 8}

Test- the- Test Can't remember how to solve absolute value equations? Don't ™‘””›ǡ ›‘—…ƒ •–‹ŽŽ ‰‡– –Š‹• problem correct! ‹’Ž› ’Ž—‰ ‹ –Š‡ answer choices into the absolute value equation to determine which ˜ƒŽ—‡• ›‹‡Ž† ƒ ƒ–Š‡ƒ–‹…ƒŽŽ› correct statement.

If ( ) f x ( ) f x

, for what value of x

is

( —†‡ϐ‹‡†ǫ x x − − − 2 = ( ) 1 2

15.

)

Ǥ 2 B. 1 C. 0 D. 1 E. 2