Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Compare the steepness of the following functions. How does [tex]$f_4$[/tex] compare to [tex]$f_1$[/tex]?

\begin{tabular}{|c|c|c|c|}
\hline
[tex]$f_1(x)=2x$[/tex] & [tex]$f_2(x)=5x$[/tex] & [tex]$f_3(x)=0.5x$[/tex] & [tex]$f_4(x)=0.5x$[/tex] \\
\hline
\end{tabular}

A. Function 4 is more steep.

B. There is no difference in the function.

C. Function 4 is less steep.

D. None of the other answers are correct.

Sagot :

GinnyAnswer
To determine how [tex]\( f_4 \)[/tex] compares to [tex]\( f_1 \)[/tex] in terms of steepness, we need to analyze the slopes of both functions.

Given the functions:
- [tex]\( f_1(x) = 2x \)[/tex]
- [tex]\( f_2(x) = 5x \)[/tex]
- [tex]\( f_3(x) = 0.5x \)[/tex]
- [tex]\( f_4(x) = 0.5x \)[/tex]

The slope of a linear function [tex]\( f(x) = mx \)[/tex] is given by the coefficient [tex]\( m \)[/tex].

Step-by-step solution:

1. Identify the slopes:
- The slope of [tex]\( f_1(x) = 2x \)[/tex] is [tex]\( m_1 = 2 \)[/tex].
- The slope of [tex]\( f_2(x) = 5x \)[/tex] is [tex]\( m_2 = 5 \)[/tex].
- The slope of [tex]\( f_3(x) = 0.5x \)[/tex] is [tex]\( m_3 = 0.5 \)[/tex].
- The slope of [tex]\( f_4(x) = 0.5x \)[/tex] is [tex]\( m_4 = 0.5 \)[/tex].

2. Compare the slopes of [tex]\( f_1 \)[/tex] and [tex]\( f_4 \)[/tex]:
- The slope of [tex]\( f_1 \)[/tex] is [tex]\( 2 \)[/tex].
- The slope of [tex]\( f_4 \)[/tex] is [tex]\( 0.5 \)[/tex].

Since [tex]\( 0.5 < 2 \)[/tex],

3. Conclude the comparison:
- Function 4 is less steep than Function 1.

So, the appropriate statement is:
"Function 4 is less steep."

Thus, the correct answer to the question is:
Function 4 is less steep.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.