Algebra 2 Honors Midterm Flashcards

Questions and Answers

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?

Straight line

What is the domain of a Constant (P-Function)?

What is the range of a Constant (P-Function)?

y = c Signup and view all the answers

Where does a Constant (P-Function) intersect the y-axis?

(0, c) Signup and view all the answers

What is the function for a Linear (P-Function)?

f(x) = x Signup and view all the answers

What is the range of a Linear (P-Function)?

R Signup and view all the answers

Where does a Linear (P-Function) intersect the y-axis?

(0, 0) Signup and view all the answers

What is the standard function of a Quadratic (P-Function)?

f(x) = x^2 Signup and view all the answers

What is the shape of the graph of a Quadratic (P-Function)?

Parabola Signup and view all the answers

What is the domain of a Quadratic (P-Function)?

R Signup and view all the answers

What is the range of a Quadratic (P-Function)?

y > 0 Signup and view all the answers

Where does a Quadratic (P-Function) intersect the y-axis?

(0, 0) Signup and view all the answers

What is the function for a Cubic (P-Function)?

f(x) = x^3 Signup and view all the answers

What is the shape of the graph of a Cubic (P-Function)?

Two halves of a parabola Signup and view all the answers

What is the domain of a Cubic (P-Function)?

R Signup and view all the answers

What is the range of a Cubic (P-Function)?

R Signup and view all the answers

Where does a Cubic (P-Function) intersect the y-axis?

(0, 0) Signup and view all the answers

What is the function for a Square Root (P-Function)?

f(x) = square root of x Signup and view all the answers

What is the slope of the graph of a Square Root (P-Function)?

Upwards slope Signup and view all the answers

What is the domain of a Square Root (P-Function)?

x > 0 Signup and view all the answers

What is the range of a Square Root (P-Function)?

y > 0 Signup and view all the answers

Where does a Square Root (P-Function) intersect the y-axis?

(0, 0) Signup and view all the answers

How can more data points help in identifying parent functions?

Increases accuracy Signup and view all the answers

What is helpful to remember about vertical and horizontal translations?

Add to y, go high; add to x, go left Signup and view all the answers

In a horizontal stretch or compression, what happens to y-intercepts?

They stay the same Signup and view all the answers

In a vertical stretch or compression, what happens to x-intercepts?

They stay the same Signup and view all the answers

The correlation coefficient $r$ is a value in the range _____

-1 to 1 Signup and view all the answers

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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Description

Prepare for your Algebra 2 Honors midterm exam with these flashcards covering key polynomial functions. Each card includes the function type, definition, and graphical characteristics, helping you solidify your understanding and readiness for the test.