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.
