What is the range of the relation [tex]\{(1, 2), (2, 4), (3, 2), (4, 6)\}[/tex]?
A. \{2, 4\}
B. \{1, 2, 3, 4, 6\}
C. \{2, 4, 6\}
D. \{1, 2, 3, 4\}
---
Which relation is a function?
A. \{(1, 2), (2, 3), (3, 4), (2, 5)\}
B. \{(1, 2), (1, 3), (1, 4), (1, 5)\}
C. \{(1, 2), (2, 3), (3, 4), (1, 5)\}
D. \{(1, 2), (2, 2), (3, 2), (4, 2)\}
---
For the function [tex]f(x) = 2 - 3x[/tex], find [tex]f(4)[/tex].
A. -5
B. 12
C. -10
D. 14
---
Which equation represents a direct linear variation?
A. [tex]y = x - 3[/tex]
B. [tex]y = \frac{1}{3}x[/tex]
C. [tex]y = x^2[/tex]
D. [tex]y = \frac{1}{x}[/tex]
---
Which is the direct linear variation equation for the relationship?
[tex]y[/tex] varies directly with [tex]x[/tex] and [tex]y = 12[/tex] when [tex]x = 4[/tex].
A. [tex]y = 3^x[/tex]
B. [tex]y = x + 8[/tex]
C. [tex]y = 2x + 4[/tex]
D. [tex]y = x - 8[/tex]
---
Which is the quadratic variation equation for the relationship?
[tex]y[/tex] varies directly with [tex]x^2[/tex] and [tex]y = 48[/tex] when [tex]x = 2[/tex].
A. [tex]y = 4x^2[/tex]
B. [tex]y = 4x[/tex]
C. [tex]y = 12x^2[/tex]
D. [tex]y = x^2 + 25[/tex]
---
Write the inverse variation equation for the relationship:
[tex]y[/tex] varies inversely with [tex]x[/tex] and [tex]y = 4[/tex] when [tex]x = 2[/tex].
A. [tex]y = 2x[/tex]
B. [tex]y = \frac{8}{x}[/tex]
C. [tex]y = x + 2[/tex]
D. [tex]y = \frac{1}{2}x[/tex]
Answer (2)
( 1 ) r an g e : { 2 , 4 , 6 } ⇒ A n s . C ( 2 ) f u n c t i o n : {( 1 , 2 ) ; ( 2 , 2 ) ; ( 3 , 2 ) ; ( 4 , 2 )} ⇒ A n s . D ( 3 ) f ( 4 ) = 2 − 3 ⋅ 4 = 2 − 12 = − 10 ⇒ A n s . C ( 4 ) d i rec t : y = a x ⇒ y = 3 1 x ⇒ A n s . B ( 5 ) f ( x ) = a x an d f ( 4 ) = 12 . ⇒ 12 = a ⋅ 4 ⇒ a = 3 ⇒ f ( x ) = 3 x ⇒ A n s . ( ?)
( 6 ) f ( x ) = a x 2 an d f ( 2 ) = 48 . ⇒ 48 = a ⋅ 2 2 ⇒ a = 48 : 4 = 12 ⇒ f ( x ) = 12 x 2 ⇒ A n s . C ( 7 ) in v erse l y : f ( x ) = x a an d f ( 2 ) = 4 . ⇒ 4 = 2 a ⇒ a = 4 ⋅ 2 = 8 ⇒ y = x 8 ⇒ A n s . B
The range of the relation is {2, 4, 6} (C). The function is {(1, 2), (2, 2), (3, 2), (4, 2)} (D). For f ( 4 ) , the result is -10 (C). The direct linear variation is y = 3 1 x (B). The quadratic equation is y = 12 x 2 (C), and the inverse variation is y = x 8 (B).
;
