Question

Which of the following statements is (are) CORRECT for a constant function?

• A. It is a function whose range consists of only one element
• B. It is a type of polynomial function having degree $0$
• C. Its graph is a line which is always parallel to $x-$axis.
• D. Domain of constant function is $R$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A It is a function whose range consists of only one element
B It is a type of polynomial function having degree $0$
C Its graph is a line which is always parallel to $x-$axis.
D Domain of constant function is $R$

Constant function is of the form $f\left(x\right)=c$
It is defined for every real value of $x$ and for every real value as input, it gives a fixed constant value as output.
So, its domain is $R$ and its range consists of only one element, for example $f\left(x\right)=5$ has range $=\left\{5\right\}$.

It can be represented in the form of polynomial function $f\left(x\right)=x^{n}c$, where in this case $n=0$.

Graph of $y=c$ can be plotted as