Answered

IDNLearn.com: Your one-stop destination for reliable answers to diverse questions. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.

Select the correct answer.

This table models function [tex]\( m \)[/tex].

[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -2 & 0 & 2 & 4 \\
\hline
m(x) & 4 & -6 & 0 & 70 \\
\hline
\end{array}
\][/tex]

Function [tex]\( n \)[/tex] represents a cubic function that passes through the points [tex]\((-1,0)\)[/tex] and [tex]\((0,2)\)[/tex]. Which statement is true?

A. The [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex] is less than the [tex]\( y \)[/tex]-intercept of [tex]\( n \)[/tex].

B. The [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex] is equal to the [tex]\( y \)[/tex]-intercept of [tex]\( n \)[/tex].

C. The [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex] is greater than the [tex]\( y \)[/tex]-intercept of [tex]\( n \)[/tex].

D. The [tex]\( y \)[/tex]-intercept of [tex]\( m \)[/tex] is not given.

Sagot :

GinnyAnsweridn
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].
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.