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Question 1 of 11

A bird flies south. Its distance from its nest, as a function of time, is modeled by [tex] y = 20x + 1 [/tex].

Which statement best describes the function?

A. The function is nonlinear.
B. Not enough information is given to decide.
C. The function is linear.
D. The function is linear at some points and nonlinear at other points.

Sagot :

GinnyAnsweridn
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.
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