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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.



Answer :

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.

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