To determine the correct answer, follow these steps:
1. Identify the [tex]\( y \)[/tex]-intercept of function [tex]\( m \)[/tex] from the table:
The table provided shows values of [tex]\( m(x) \)[/tex] for different [tex]\( x \)[/tex]. The [tex]\( y \)[/tex]-intercept of a function is the value of the function at [tex]\( x = 0 \)[/tex].
- From the table, when [tex]\( x = 0 \)[/tex], [tex]\( m(x) = -6 \)[/tex].
- Therefore, the [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex] is [tex]\( -6 \)[/tex].
2. Identify the [tex]\( y \)[/tex]-intercept of function [tex]\( n \)[/tex]:
Function [tex]\( n \)[/tex] is a cubic function that passes through the point [tex]\( (0, 2) \)[/tex].
- The [tex]\( y \)[/tex]-intercept of a function is the value of the function at [tex]\( x = 0 \)[/tex].
- Given point [tex]\( (0, 2) \)[/tex] indicates that when [tex]\( x = 0 \)[/tex], [tex]\( n(x) = 2 \)[/tex].
- Therefore, the [tex]\( y \)[/tex]-intercept of [tex]\( n \)[/tex] is [tex]\( 2 \)[/tex].
3. Compare the [tex]\( y \)[/tex]-intercepts of [tex]\( m \)[/tex] and [tex]\( n \)[/tex]:
- The [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex] is [tex]\( -6 \)[/tex].
- The [tex]\( y \)[/tex]-intercept of [tex]\( n \)[/tex] is [tex]\( 2 \)[/tex].
Since [tex]\( -6 \)[/tex] (the [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex]) is less than [tex]\( 2 \)[/tex] (the [tex]\( y \)[/tex]-intercept of [tex]\( n \)[/tex]), we conclude that:
A. The [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex] is less than the [tex]\( y \)[/tex]-intercept of [tex]\( n \)[/tex].
Thus, the correct answer is:
A. The [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex] is less than the [tex]\( y \)[/tex]-intercept of [tex]\( n \)[/tex].
