DIAGNOSTIC TEST GENERAL MATHEMATICS

Examine the following sets of ordered pairs. Which one represents a one-to-one relation?

• $\left(1,-1\right),\ \left(1,1\right),\ \left(2,4\right),\ \left(2,\ 6\right)$

• $\left(2,0\right),\ \left(3,1\right),\ \left(2,1\right),\ \left(4,-3\right)$

• $\left(-2,\ 3\right),\ \left(-1,1\right),\ \left(0,0\right),\ \left(2,1\right)$

• $\left(-1,-1\right),\ \left(1,1\right),\left(2,3\right),\left(4,5\right)$

Which of the following equation is not a function?

• $f\left(x\right)\ =\ 2x\ -3$

• $f\left(x\right)\ =\ \sqrt{x}$

• $y^2=2x$

• $y\ =\ \frac{x\ -\ 3}{x\ +\ 1}$

Using $f\left(x\right)\ =\ x\ -2\$    and  $g\left(x\right)\ =\ 5x\ +\ 3,$   find  $f\left(g\left(2\right)\right)?$  

• 3

• 9

• 11

• 13

 $f\left(x\right)\ =\ -3x-6$  and  $g\left(x\right)\ =\ 5x\ +2.$  Find  $f\left(x\right)\ +\ g\left(x\right).$  

Let

•  $2x-4$  

•  $-8x-8$  

•  $-8x-4$  

•  $2x-8$  

Let

 $f\left(x\right)\ =3x\ +\ 2\$  and  $g\left(x\right)\ =\ x-3.$  Find  $f\left(x\right)\ -g\left(x\right).$  

•  $2x-5$  

•  $2x+5$  

•  $4x-1$  

•  $2x-1$  

 $Let\ f\left(x\right)\ =x^2\ +2x-1$  and  $g\left(x\right)=2x-4$ 

Find  $2\left(f\left(x\right)\right)-3\left(g\left(x\right)\right)$  

•  $2x^2-2x-14$  

•  $2x^2-2x+10$  

•  $-3x^2-2x-1$  

•  $-3x^2-2x-7$  

 $f\left(x\right)=5x^2-7x+3\ and\ g\left(x\right)=\ 4x\ +\ 9.\$  

Given the following functions. Evaluate  $\left(f\circ\ g\right)\left(x\right)?$  

•  $-8x-15$  

•  $30x^2+332x+345$  

•  $80x^2+332x+345$  

•  $80x^2+152x+345$  

 $If\ f\left(x\right)\ =\ 5x^2-7x+3\ and\ g\left(x\right)\ =4x\ +9$  

Evaluate  $\left(f+g\right)\left(x\right)?$  

•  $5x^2-11x+12$  

•  $5x^2+3x+12$  

•  $5x^2-3x+12$  

•  $5x^2-2x+12$  

 $Let\ f\left(x\right)\ =3x+2\ and\ g\left(x\right)=7x+6$  

Find  $f\left(x\right)\ \cdot\ g\left(x\right)$  and its domain.

•  $6x^2+4x+42;\$  all real numbers except  $x=-\frac{2}{3}$  

•  $6x^2+4x+42;$  all real numbers

•  $21x^2+32x+12;$  all real numbers

•  $21x^2+32x+12;$  all real numbers except  $x=-\frac{6}{7}$  

 $Let\ f\left(x\right)=3x-6\ and\ g\left(x\right)=x-2.\ Find\ \frac{f\left(x\right)}{g\left(x\right)}$  and its domain.

• 3; all real numbers

• 3; all real numbers except x=2

• 1; all real numbers

• -3; all real numbers except x = 3