Question

Identity the function to which f(x) belongs. f(x) = 2.

a) Linear function
b) Quadratic function
c) Constant function
d) Exponential function

Answer 1

The function f(x) = 2 is a constant function because its value does not change with different values of x. Its graph is a horizontal line, distinguishing it from linear, quadratic, and exponential functions.

Step-by-step explanation:

The student has asked us to identify the function to which f(x) = 2 belongs. This equation represents a function where the value of f(x) does not change regardless of the value of x. Therefore, it is a constant function.

Each function type has distinct characteristics:

• Linear functions have the form y = mx + b, where the graph is a straight line with slope m.
• Quadratic functions are second-order polynomials with the form y = ax² + bx + c, where the graph is a parabola.
• Exponential functions take the form y = a*b¹¹, where the base b is a constant and the graph shows exponential growth or decay.

In the case of f(x) = 2, the graph would be a horizontal line, which is characteristic of a constant function. Therefore, the correct answer is c) Constant function.