Introduction to Functions

Q.

Can there be two absolute maximums?

Q.

Write a function rule for “the output is three less than the input.”

Q. Every relation is a function.

1. True
2. False

Q. Consider relations between two sets $X$ and $Y$ where $x$ belongs to $X$ and $y$ belongs $Y$, find which of the following relation from $X$ to $Y$ is a function.

1. $x-y=2$
2. $x^2+y^2=8$
3. $\left\{\right(2,3),(2,4\left)\right\}$
4. All of the above.

Q. For a relation to be a function, each input results in

1. More than one outputs
2. Only one output
3. Any number of outputs
4. None of the above

Q. Which of the following statements is correct-

1. All Relations are Functions
2. All Functions are Relations
3. Some Functions are NOT Relations
4. Some Relations are NOT Functions

Q. Relation between set X and set Y in which each element of set X is associated with exactly one element of set Y is known as

Q. Two sets $X$ and $Y$ are given such that
$X=\{54,79,38\}\&Y=\{32,44,86\}$. Which of the below relations from set $X$ to set $Y$ are functions?

1. $f_1=\left\{\right(54,32),(79,44),(38,86\left)\right\}$
2. $f_2=\left\{\right(54,32),(54,44),(79,44),(38,86\left)\right\}$
3. $f_3=\left\{\right(54,86),(38,32\left)\right\}$
4. All are functions

Q. Avnish started from his home at $8:00\text{A.M.}$at a constant speed of $500$m/min. His office is $3$ km away from his home. Which of the below shows function from the set of time taken(in min) to the set of distance covered by him(in Km)?

1. $\left\{\right(1,0.5\text{km}),(2,1\text{km}),(3,1.5\text{km}),(4,2\text{km}),(5,2.5\text{km}),(6,3\text{km}\left)\right\}$
2. $\left\{\right(1,0.5\text{km}),(2,1\text{km}),(3,1.5\text{km}),(4,2\text{km}\left)\right\}$
3. (a) and (b) both
4. None of the above