Sample quiz on function definition
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1. Which of the following statements is correct?
   
   Relations and functions are the same
   Every relation is also a function
   Every function is a relation
   Every relation with range $\mathbb{R}$ is a function.
2. Which of the following equations doesn't represent a function?
   
   $y=\pm\sqrt{x}$
   $y=\sqrt{x}$
   $y=x^2$
   $y=x$
3. Which of the following relations is a function?
   
   $x^2-y=0$
   $x^2+y^2=1$
   $x^2-y^2=1$
   $x^2-y^2=4$
   
4. In order to check if a graph represents a function, one uses $\cdots$?
   
   the horizontal line test
   the vertical line test
   the slanted line test
   the line symmetry test
5. If the ordered pairs $\{(a,1),(2,3),(4,5),(6,7)\}$ is a function, which restriction is unnecessary?
   
   $a\neq 6$
   $a\neq 4$
   $a\neq 2$
   $a\neq 1$
6. If the ordered pairs $\{(a,1),(2,3),(4,5),(6,7)\}$ is a function, which restriction is necessary?
   
   $a\neq 5$
   $a\neq 3$
   $a\neq 2$
   $a\neq 1$
7. Which of the following equations represents a relation that is not a function?
   
   $x^2-y=1$
   $x^2-y^2=1$
   $x^2-2y=1$
   $x^2+2y=1$
8. If the ordered pairs $\{(1,a),(1,2),(-2,b-a),(-2,0)\}$ define a function, find $a$ and $b$.
   
   $a=1,b=2$
   $a=2,b=1$
   $a=1,b=1$
   $a=2,b=2$
9. Do the ordered pairs $\{(1,1),(2,1),(3,1),(4,1),(5,1)\}$ represent a function?
   
   No, because $1$ was repeated a lot
   Yes, it is a constant function
   No, because its graph is vertical
   Not sure to be honest
10. Which of the following is a way of representing functions?
    
    Using mapping diagrams
    Using graphs
    Using equations
    All of the above