To compare the functions \( f(x) = x \) and \( f(x) = 3x - 4 \):
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Slope Comparison:
- The slope of the line \( f(x) = x \) is \( 1 \).
- The slope of the line \( f(x) = 3x - 4 \) is \( 3 \).
- Thus, the slope increases by a factor of \( 3 \) (from \( 1 \) to \( 3 \)).
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Y-intercept Comparison:
- The y-intercept of the line \( f(x) = x \) is \( 0 \) (it crosses the y-axis at (0,0)).
- The y-intercept of the line \( f(x) = 3x - 4 \) is \( -4 \) (it crosses the y-axis at (0,-4)).
- Therefore, the graph of the function moves down the y-axis by \( 4 \) units.
Putting this together, the correct response is:
The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.