Podcast
Questions and Answers
What is the rule for a Constant (P-Function)?
What is the rule for a Constant (P-Function)?
- f(x) = x^2
- f(x) = x
- f(x) = c (correct)
- f(x) = x^3
What does the graph of a Constant (P-Function) look like?
What does the graph of a Constant (P-Function) look like?
Straight line
What is the domain of a Constant (P-Function)?
What is the domain of a Constant (P-Function)?
R
What is the range of a Constant (P-Function)?
What is the range of a Constant (P-Function)?
Where does a Constant (P-Function) intersect the y-axis?
Where does a Constant (P-Function) intersect the y-axis?
What is the function for a Linear (P-Function)?
What is the function for a Linear (P-Function)?
What is the range of a Linear (P-Function)?
What is the range of a Linear (P-Function)?
Where does a Linear (P-Function) intersect the y-axis?
Where does a Linear (P-Function) intersect the y-axis?
What is the standard function of a Quadratic (P-Function)?
What is the standard function of a Quadratic (P-Function)?
What is the shape of the graph of a Quadratic (P-Function)?
What is the shape of the graph of a Quadratic (P-Function)?
What is the domain of a Quadratic (P-Function)?
What is the domain of a Quadratic (P-Function)?
What is the range of a Quadratic (P-Function)?
What is the range of a Quadratic (P-Function)?
Where does a Quadratic (P-Function) intersect the y-axis?
Where does a Quadratic (P-Function) intersect the y-axis?
What is the function for a Cubic (P-Function)?
What is the function for a Cubic (P-Function)?
What is the shape of the graph of a Cubic (P-Function)?
What is the shape of the graph of a Cubic (P-Function)?
What is the domain of a Cubic (P-Function)?
What is the domain of a Cubic (P-Function)?
What is the range of a Cubic (P-Function)?
What is the range of a Cubic (P-Function)?
Where does a Cubic (P-Function) intersect the y-axis?
Where does a Cubic (P-Function) intersect the y-axis?
What is the function for a Square Root (P-Function)?
What is the function for a Square Root (P-Function)?
What is the slope of the graph of a Square Root (P-Function)?
What is the slope of the graph of a Square Root (P-Function)?
What is the domain of a Square Root (P-Function)?
What is the domain of a Square Root (P-Function)?
What is the range of a Square Root (P-Function)?
What is the range of a Square Root (P-Function)?
Where does a Square Root (P-Function) intersect the y-axis?
Where does a Square Root (P-Function) intersect the y-axis?
How can more data points help in identifying parent functions?
How can more data points help in identifying parent functions?
What is helpful to remember about vertical and horizontal translations?
What is helpful to remember about vertical and horizontal translations?
In a horizontal stretch or compression, what happens to y-intercepts?
In a horizontal stretch or compression, what happens to y-intercepts?
In a vertical stretch or compression, what happens to x-intercepts?
In a vertical stretch or compression, what happens to x-intercepts?
The correlation coefficient $r$ is a value in the range _____
The correlation coefficient $r$ is a value in the range _____
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Study Notes
Parent Functions
-
Constant Function (P-Function):
- Defined by f(x) = c
- Graph is a straight line
- Domain is all real numbers (R)
- Range is a single value: y = c
- Intersects Y-axis at point (0, c)
-
Linear Function (P-Function):
- Defined by f(x) = x
- Graph is a diagonal line through the origin
- Domain is all real numbers (R)
- Range is all real numbers (R)
- Intersects at point (0, 0)
-
Quadratic Function (P-Function):
- Defined by f(x) = x²
- Graph is a parabola opening upwards
- Domain is all real numbers (R)
- Range is y > 0
- Intersects at point (0, 0)
-
Cubic Function (P-Function):
- Defined by f(x) = x³
- Graph consists of two halves of a parabola
- Domain is all real numbers (R)
- Range is all real numbers (R)
- Intersects at point (0, 0)
-
Square Root Function (P-Function):
- Defined by f(x) = √x
- Graph shows an upward slope
- Domain is x > 0
- Range is y > 0
- Intersects at point (0, 0)
Helpful Tips
-
Identifying Parent Functions:
- A greater number of data points improves the accuracy of matching to a parent function.
-
Transforming Linear Functions:
- For translations: "Add to y, go high; Add to x, go left."
-
Intercept Properties:
- Horizontal stretches/compressions do not affect y-intercepts.
- Vertical stretches/compressions do not affect x-intercepts.
Correlation Coefficient Properties
- The correlation coefficient, denoted as r, ranges from -1 to 1.
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