The graph of which function is decreasing over the interval (–4, [infinity])? f(x) = (x 4)2 4 f(x) = –(x 4)2 4 f(x) = (x – 4)2 –
1 answer:
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Answer:
- No, the points are evenly distributed about the x-axis.
Explanation:
<u>1. Write the table with the data:</u>
x given predicted residual
1 - 3.5 - 1.1
2 - 2.9 2
3 - 1.1 5.1
4 2.2 8.2
5 3.4 1.3
<u>2. Complete the column of residuals</u>
The residual is the observed (given) value - the predicted value.
- residual = given - predicted.
Thus, the complete table, with the residual values are:
x given predicted residual
1 - 3.5 - 1.1 - 2.4
2 - 2.9 2 - 4.9
3 - 1.1 5.1 - 6.2
4 2.2 8.2 - 6.0
5 3.4 1.3 2.1
<u>3. Residual plot</u>
You must plot the last column:
x residual
1 - 2.4
2 - 4.9
3 - 6.2
4 - 6.0
5 2.1
See the plot attached.
<em>Does the residual plot show that the line of best fit is appropriate for the data?</em>
Ideally, a residual plot for a line of best fit that is appropiate for the data must not show any pattern; the points should be randomly distributed about the x-axis.
But the points of the plot are not randomly distributed about the x-axis: there are 4 points below the x-axis and 1 point over the x-axis: there are more negative residuals than positive residuals. This is a pattern. Also, you could say that they show a curve pattern, which drives to the same conclusion: the residual plot shows that the line of best fit is not appropiate for the data.
Thus, the conclusion should be: No, the points have a pattern.
- 1. "<em>Yes, the points have no pattern</em>": false, because as shown, the points do have a pattern, which makes the residual plots does not show that the line of best fit is appropiate for the data.
- 2. "<em>No, the points are evenly distributed about the x-axis</em>": true. As already said the points have a pattern. It is a curved pattern, and this <em>shows the line of best fit is not appropiate for the data.</em>
- 3. "<em>No, the points are in a linear pattern</em>": false. The points are not in a linear pattern.
- 4. "<em>Yes, the points are in a curved pattern</em>": false. Because the points are in a curved pattern, the residual plot shows that the line of best fit is not appropiate for the data.
