Answer :
To compare how the graph of the new function [tex]\( y = x - 1 \)[/tex] compares with the original function [tex]\( y = x + 2 \)[/tex], we need to look at how their equations differ and what that implies about their graphs.
1. Identify and Compare the Functions:
- The original function is [tex]\( y = x + 2 \)[/tex].
- The new function is [tex]\( y = x - 1 \)[/tex].
2. Analyze the Changes:
- Both functions are linear and of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- In [tex]\( y = x + 2 \)[/tex], the slope [tex]\( m = 1 \)[/tex] and the y-intercept [tex]\( b = 2 \)[/tex].
- In [tex]\( y = x - 1 \)[/tex], the slope [tex]\( m = 1 \)[/tex] and the y-intercept [tex]\( b = -1 \)[/tex].
3. Compare Slopes:
- Both functions have the same slope, [tex]\( m = 1 \)[/tex]. This means the lines are parallel and equally steep.
4. Compare Intercepts:
- The original function intersects the y-axis at [tex]\( y = 2 \)[/tex].
- The new function intersects the y-axis at [tex]\( y = -1 \)[/tex].
5. Determine the Transformation:
- Since both lines have the same slope, the only difference between the two graphs is the vertical shift due to the difference in y-intercepts.
- The y-intercept changes from 2 to -1. This represents a shift down by 3 units (because [tex]\( -1 - 2 = -3 \)[/tex]).
Therefore, the graph of the new function [tex]\( y = x - 1 \)[/tex] is obtained by shifting the graph of [tex]\( y = x + 2 \)[/tex] down by 3 units.
The correct answer is:
A. It would be shifted down.
1. Identify and Compare the Functions:
- The original function is [tex]\( y = x + 2 \)[/tex].
- The new function is [tex]\( y = x - 1 \)[/tex].
2. Analyze the Changes:
- Both functions are linear and of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- In [tex]\( y = x + 2 \)[/tex], the slope [tex]\( m = 1 \)[/tex] and the y-intercept [tex]\( b = 2 \)[/tex].
- In [tex]\( y = x - 1 \)[/tex], the slope [tex]\( m = 1 \)[/tex] and the y-intercept [tex]\( b = -1 \)[/tex].
3. Compare Slopes:
- Both functions have the same slope, [tex]\( m = 1 \)[/tex]. This means the lines are parallel and equally steep.
4. Compare Intercepts:
- The original function intersects the y-axis at [tex]\( y = 2 \)[/tex].
- The new function intersects the y-axis at [tex]\( y = -1 \)[/tex].
5. Determine the Transformation:
- Since both lines have the same slope, the only difference between the two graphs is the vertical shift due to the difference in y-intercepts.
- The y-intercept changes from 2 to -1. This represents a shift down by 3 units (because [tex]\( -1 - 2 = -3 \)[/tex]).
Therefore, the graph of the new function [tex]\( y = x - 1 \)[/tex] is obtained by shifting the graph of [tex]\( y = x + 2 \)[/tex] down by 3 units.
The correct answer is:
A. It would be shifted down.
