To determine the nature of the function, let's analyze its given form:
The function representing the distance [tex]\( y \)[/tex] of the bird from its nest over time [tex]\( x \)[/tex] is [tex]\( y = 20x + 1 \)[/tex].
This function can be compared to the standard form of a linear equation, which is [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept.
In the function [tex]\( y = 20x + 1 \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] is 20, which acts as the slope (m).
- The constant term is 1, which acts as the y-intercept (b).
Key characteristics of a linear function include:
1. The graph of a linear function is a straight line.
2. The rate of change (slope) is constant throughout the function.
Given that the form [tex]\( y = 20x + 1 \)[/tex] perfectly matches the structure of a linear equation [tex]\( y = mx + b \)[/tex], it indicates that the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is indeed linear.
Thus, the correct statement that best describes the function is:
C. The function is linear.
