Question

What is the range of the relation? {(1, 2), (2, 4), (3, 2), (4, 6)}    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 f(x) = 2 – 3x, find f(4).    A. –5    B. 12    C. –10    D. 14
Which equation represents a direct linear variation?    A. y = x – 3    B.y=1/3x    C. y = x^2    D.y=1/x
Which is the direct linear variation equation for the relationship?

y varies directly with x and y = 12 when x = 4.
     A. y = 3^x    B. y = x + 8    C. y = 2x + 4      D. y = x – 8
Which is the quadratic variation equation for the relationship?

    y varies directly with x2 and y = 48 when x = 2.
     A. y = 4x^2    B. y = 4x    C. y = 12x^2    D. y = x^2 + 25

Write the inverse variation equation for the relationship:  y varies inversely with x and y = 4 when x = 2.    A. y = 2x    B.y=8/x    C. y = x + 2    D.y=1/2x

Answer 1

`(1)\ \ \ \ range:\ \ \ \{2, 4, 6\}\ \ \ \Rightarrow\ \ \ Ans.\ C\\\\(2)\ \ \ function:\ \ \ \{(1, 2); (2, 2); (3, 2); (4, 2)\}\ \ \ \Rightarrow\ \ \ Ans.\ D\\\\(3)\ \ \ f(4)=2-3\cdot4=2-12=-10\ \ \ \Rightarrow\ \ \ Ans.\ C\\\\(4)\ \ \ direct:\ \ \ y=ax\ \ \ \Rightarrow\ \ \ y= (1)/(3) x\ \ \ \Rightarrow\ \ \ Ans.\ B\\\\(5)\ \ \ f(x)=ax\ \ \ and\ \ \ f(4)=12\\.\ \ \ \ \ \Rightarrow\ \ \ 12=a\cdot4\ \ \ \Rightarrow\ \ \ a=3\ \ \ \Rightarrow\ \ \ f(x)=3x\ \ \ \Rightarrow\ \ \ Ans.\ (?)\\\\`


`(6)\ \ \ f(x)=ax^2\ \ \ and\ \ \ f(2)=48\\.\ \ \ \Rightarrow\ \ 48=a\cdot2^2\ \ \Rightarrow\ \ a=48:4=12\ \ \Rightarrow\ \ f(x)=12x^2\ \Rightarrow\ \ Ans.\ C\\\\(7)\ \ \ inversely:\ \ \ f(x)= (a)/(x) \ \ \ and\ \ \ f(2)=4\\.\ \ \ \Rightarrow\ \ \ 4= (a)/(2) \ \ \ \Rightarrow\ \ \ a=4\cdot2=8\ \ \ \Rightarrow\ \ \ y= (8)/(x)\ \ \ \Rightarrow\ \ \ Ans.\ B`