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Assignment: Positive and Negative Parts and Increasing and Decreasing
Intervals
Part I: Analyzing a Graph
For each graph below, identify any interval(s) where the rational function is a) positive, b)
negative, c) increasing, and/or d) decreasing. Use inequality signs where appropriate, and write
“none” if any of the characteristics do not apply.
1.
function is undefined at 1
x >1
a) positive: __________
x -2
b) negative: __________
x ≠ -2
c) increasing: __________
none
d) decreasing: __________
© K12 Inc.
3.
The function appears to be undefined
for x=0.
x≠0
a) positive: __________
none
b) negative: __________
x0
d) decreasing: __________
© K12 Inc.
Part II: Draw Your Own Graph
Follow the directions to draw the graph of a function that meets the description.
4. Draw the graph of a rational function that is positive for x < 2 and negative for x > 2 on the
coordinate plane below.
© K12 Inc.
5. Draw the graph of a rational function that is increasing for x < –4 and decreasing for x > –4 on
the coordinate plane below.
© K12 Inc.
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Generate a scatterplot for the specified dependent variable (Y) and the selected independent variable (X), including the graph of the "best fit" line. Interpret.
Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable.
Determine the coefficient of correlation. Interpret.
Determine the coefficient of determination. Interpret.
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Compute the confidence interval for b, using a 95% confidence level. Interpret this interval.
Compute the 99% confidence interval for the dependent variable, for a selected value of the independent variable. Each student can choose a value to use for the independent variable (use same value in the next step). Interpret this interval.
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