Question

If y is expressed in terms of a variable x as $ y=f(x) $ , then y is called:
A. Explicit function.
B. Implicit function.
C. Linear function.
D. Identity function.

Answer 1

Hint: An implicit function is a function written in terms of both dependent and independent variables. For example, $ y-3xy+2x+5=0 $ .
Whereas an explicit function is a function which is represented in terms of an independent variable. For example, $ y=3x+1 $ is explicit where y is a dependent variable and x is the independent variable.
A Linear function can be either implicit or explicit with the highest degree of any term as 1. For example, $ x+2y-3=0 $ or $ y=4x+3 $ etc.
An identity function is a function that always returns the same value that was used as its argument. i.e. $ y=f(x)=x $ .

Complete step-by-step answer:
In the given function $ y=f(x) $ , y is the dependent variable and x is the independent variable, and both the variables do not occur together.
Since the variable y is represented in terms of the independent variable x only, this is the case of an explicit function.
The correct answer is, therefore, B. Explicit function.

Note: An independent variable is the one whose value we choose, and the other variables become the dependent variables because their values depend upon the choice of the value of the independent variable.
Implicit functions are usually represented as $ f(x,y)=0 $ .
Explicit functions are represented as $ y=f(x) $ . [or $ x=f(y) $ ].
Usually, it is possible to express a quadratic, cubic or 4th degree implicit function as an explicit function, but the same is generally not true for higher order functions.
An identity function is also called an identity relation or identity map or identity transformation and its graph is straight line at an angle of 45˚ with the positive direction of the x-axis.