Functions
Which relation is a function?
A) ( (1, 0), (3, 0), (1, 1), (3, 1) )
B) ( (1, 1), (2, 2), (3, 3), (4, 4), (5, 8) )
C) ( (2, 7), (6, 5), (4, 4), (3, 3), (2, 1) )
D) ( (9, -3), (9, 3), (4, -2), (4, 2), (0, 0) )
B) ( (1, 1), (2, 2), (3, 3), (4, 4), (5, 8) )
Write a linear function ( f ) that determines Jack's pay if he earns a set amount plus an hourly wage.
F(x) = 10x + 8
Identify the domain and range of the relation ( {(2, 8), (30, 46), (-1, 9), (16, 3)} ).
Domain: {-1,2,16,30}
Range: {3,8,9,46}
Which of the following equations is the best trend line for Yumiko's exercise data?
A) ( y = 6x + 12 )
B) ( y = 8x + 15 )
C) ( y = 6x + 6 )
D) ( y = 8x + 8 )
D) ( y = 8x + 8 )
What is linear regression used for in statistics?
To see if a line of fit is the best fit for the data.
What is the best description of the relation: ( {(2, 8), (30, 46), (-1, 9), (16, ?)} )?
A) A function that is one-to-one
B) A function that is many-to-one
C) A function that is one-to-many
D) A relation that is not a function
A) A function that is 0ne to one
What is a reasonable domain for the function you wrote in the previous question?
A) ( 0 < x < 6 )
B) ( 0 < x < 24 )
C) ( 0 < x < 68 )
D) ( 0 < x < 248 )
A) ( 0 < x < 6 )
What does the ( y )-intercept of the line in a scatter plot represent?
A) Average time spent doing sit-ups
B) Average time spent running
C) Total time spent running
D) Average distance run
A) Average time spent doing sit-ups
What does the trend line represent in a scatter plot?
Positive Correlation
How do you calculate the slope of a linear regression line using two points?
y2-y1/x2-x1 or Change in y's/Change in x's
Given ( f(x) = -x + 6 ) and ( g(x) = f(x + 3) ), write an equation for function ( g ).
g(x)= -x +3
If Jack works from 2:30 p.m. to 7:00 p.m., how much would he earn?
A) $33
B) $35.50
C) $45
D) $53
D) $53
Explain what the domain and range tell you about a function.
Domain tells us what x values we are using and how far it stretches on the x-axis.
Range tells us what y values we are using and how high it stretches on the y-axis.
Estimate the time it will take Yumiko to run 5 miles based on the data provided.
48
Explain what ( r )-value suggests a weak positive correlation.
A) ( r = 0.17454 )
B) ( r = -0.17454 )
C) ( r = 0.98264 )
D) ( r = -0.98264 )
A) ( r = 0.17454 )
For any linear function ( f(x) = mx + b ), when does ( 5f(x) = f(5x) + 5 )?
A) When ( b = 0 )
B) When ( b = 5 )
C) When ( b = 5/4 )
D) Always
C) When ( b = 5/4 )
Given ( g(x) = f(x) + k ), identify a value of ( k ) that transforms ( f ) into ( g ).
-5
What type of correlation does the scatter plot for Yumiko's running show?
A) Positive
B) Negative
C) Cannot tell
D) None
A) Positive
Is the estimate of time in the previous question an interpolation or an extrapolation?
Extrapolation
Describe how you would use linear regression to predict future values.
You can find a line of best fit to represent the direction the points are heading. It will give you an estimate value.
Which of the following is an arithmetic sequence?
A) ( -2, -5, -8, -11, -14, -17, ...)
B) ( 0, 5, 0, 10, 0, 15,.... )
C) ( 2, 4, 8, 16, 32,....)
D) ( 5, 11, 17, 23, 29, 36,.... )
A) ( -2, -5, -8, -11, -14, -17, ...)
Compute the residuals for the trend line in a scatter plot showing Yumiko's exercise time.
(-1,0,2,-2,0)
Given the data about students' heights and grade levels, determine if the data shows a positive or negative correlation.
Positive
Analyze why a trend line might not perfectly fit all data points in a scatter plot.
Because this is just an estimation it is not the actual results
Why is it important to check for outliers when performing linear regression?
They can make your residuals squared a big number and making the line not the best fit.