Compared to the graph
y=x−5
the graph
y=(x+4)−5
has been shifted
4 units down
5 units down
4 units to the right
4 units to the left
The graph y=(x+4)-5 has been shifted 4 units to the left.
The graph y = (x+4) - 5 has been shifted 5 units down compared to the graph y = x - 5.
To determine how the graph of a function has been shifted compared to another function, we can analyze the changes in the equation.
In the first equation, y = x - 5, the graph is a straight line with a slope of 1 and a y-intercept of -5. This means that the graph passes through the point (0, -5) and increases by 1 unit in the y-direction for every 1 unit increase in the x-direction.
In the second equation, y = (x + 4) - 5, the change from the first equation is the addition of (x + 4) inside the brackets. Simplifying, we have y = x + 4 - 5 = x - 1. So the second equation represents a straight line with the same slope of 1 but a different y-intercept, which is -1.
To compare the two equations and determine the shift, we can look at the y-intercepts:
In the first equation, y = x - 5, the y-intercept is -5.
In the second equation, y = x - 1, the y-intercept is -1.
Comparing the y-intercepts, we can see that the graph of y = (x + 4) - 5 has been shifted 4 units down compared to the graph of y = x - 5.
Therefore, the correct answer is that the graph y = (x + 4) - 5 has been shifted 4 units down.