Function Families and Even/Odd
What is the graph of a quadratic called?
parabola
What does adding or subtracting INSIDE the parenthesis do?
horizontal shift/ moves it left and right
What is the correlation coefficient? (a variable)
r
What is the coefficient of determination? (a variable)
r2
What pattern should the plot of the residuals have?
scattered/random
What parent function is this?
y=|x|
absolute value
What transformation occurred from the parent function f(x)=x2 to g(x)=x2+1
Vertical shift up 1 unit
Describe an r value of 0.98
(Hint: use two words)
strong positive correlation
What is the range of the coefficient of determination?
0 to 1
What is an example of what the plot of the residuals should NOT look like? (multiple correct answers)
U shaped or funnel
Is the following function even or odd?
y=x3
odd
What transformation occurred from the parent function f(x)=|x| to g(x)=-|x|
reflection over the x axis
True or false: Correlation ensures causation
FALSE
Suppose you have ran a linear, exponential, and quadratic regression and got the following r values: Which model will best represent the data?
Linear: r2=0.14
Quadratic: r2=0.74
Exponential: r2=0.82
exponential
A linear regression model was created for the set of data below. The line of best fit was found to be f(x)=1.21x-1
When x=9 what is the OBSERVED value?
x: 2, 5, 6, 7, 8, 9
y: 2, 4, 6, 8, 9, 10
10
Is the following function even or odd?
y=x4+x
neither
What transformation occurred from the parent function f(x)=x3 to g(x)=(x-3)3
Horizontal shift right 3 units
Put the following r values in order from strongest to weakest correlation:
r=0.5, r=0.98, r=-1, r=-0.8
-1, 0.98, -0.8, 0.5
Which model best represents the data?
x: 2, 5, 6, 7, 8, 9
y: 2, 4, 6, 8, 9, 10
quadratic
A linear regression model was created for the set of data below. The line of best fit was found to be f(x)=1.21x-1
When x=9 what is the PREDICTED value?
x: 2, 5, 6, 7, 8, 9
y: 2, 4, 6, 8, 9, 10
9.89
Create an example of an odd function.
Answers will vary
Write a transformation for the following function to move 3 units right and 2 units down:
f(x)=(x-2)2 +4
g(x)=(x-5)2+2
Find the r value associated with the following data: Round to the thousandth place
x: 2, 5, 6, 7, 8, 9
y: 4, 8, 2, 9, 2, 4
r=-0.103
What is the equation of the line of best fit of this data? Round to the hundredths place
x: 2, 5, 6, 7, 8, 9
y: 2, 4, 6, 8, 9, 10
y=0.06x^2+0.52x+0.54
A linear regression model was created for the set of data below. The line of best fit was found to be f(x)=1.21x-1
When x=9 what is the residual value?
x: 2, 5, 6, 7, 8, 9
y: 2, 4, 6, 8, 9, 10
0.11