To understand the differences between the function \( f(x)=x \) and Equation A \( f(x)=3x−4 \), we can analyze the changes in the slope and the vertical position (y-intercept) of the graph.
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Slope Change:
- The original function, \( f(x) = x \), has a slope of 1.
- The new equation, \( f(x) = 3x - 4 \), has a slope of 3.
- Therefore, the slope increases by a factor of 3.
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Y-Intercept Change:
- The original function intersects the y-axis at \( (0, 0) \).
- The new equation has a y-intercept of \(-4\) (it intersects the y-axis at \( (0, -4) \)).
- This indicates that the graph moves down the y-axis by 4 units.
Based on these changes, we can conclude that:
- The slope increases by a factor of 3 (from 1 to 3).
- The graph of the function moves down the y-axis by 4 units (from y=0 to y=-4).
Therefore, the correct response from the options given is:
The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.