sat suite question viewer

Algebra / Linear functions Difficulty: Hard

$x$ $x$	$f (x)$ $f (x)$
$1$ $1$	$- 64$ $negative 64$
$2$ $2$	$0$ $0$
$3$ $3$	$64$

For the linear function $f$ , the table shows three values of $x$ and their corresponding values of $f (x)$ . Function $f$ is defined by $f (x) = a x + b$ , where $a$ and $b$ are constants. What is the value of $a - b$ ?

Back question 38 of 152 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

Explanation

Choice D is correct. The table gives that $f left parenthesis x right parenthesis equals 0$ when $x equals 2$ . Substituting 0 for $f (x)$ and $2$ for $x$ into the equation $f (x) = a x + b$ yields $0 = 2 a + b$ . Subtracting $2 a$ from both sides of this equation yields $b = - 2 a$ . The table gives that $f (x) = - 64$ when $x equals 1$ . Substituting $minus 2 a$ for $b$ , $negative 64$ for $f (x)$ , and $1$ for $x$ into the equation $f (x) = a x + b$ yields $- 64 = a (1) + (- 2 a)$ . Combining like terms yields $- 64 = - a$ , or $a equals 64$ . Since $b = - 2 a$ , substituting $64$ for $a$ into this equation gives $b = (- 2) (64)$ , which yields $b = - 128$ . Thus, the value of $a - b$ can be written as $64 - (- 128)$ , which is $192$ .

Choice A is incorrect. This is the value of $a + b$ , not $a - b$ .

Choice B is incorrect. This is the value of $a minus 2$ , not $a - b$ .

Choice C is incorrect. This is the value of $2 a$ , not $a - b$ .