11.7. Polynomial Functions
Polynomials are written in the form:
where the coefficients are real numbers and the exponents are non-negative. Some examples of polynomial functions linear, quadratic, and cubic functions. High-order polynomials have a degree of 4 or more.
To graph a polynomial function:
1) If the function is defined explicitly in the form "y =," you only need to enter the function's expression. For example, enter the function "f(x) = 2x - 5" by typing in "2x - 5."
2) If the function is defined implicitly such as 2x - 3y = 4, enter the entire equation as given.
Examples
Sketch the graphs of the following polynomials:
1) y = -3
2) y = 2x - 5
3) y = -x^2 - 4x + 5
4) y = x^4 - 1
5) y = x^3 - 2x + 1
6) -3x^6 = -y - 4x + 1
Calculator solutions
Use the x^n key to enter exponents.
1) y = -3
Enter: -3
To graph a polynomial function:
1) If the function is defined explicitly in the form "y =," you only need to enter the function's expression. For example, enter the function "f(x) = 2x - 5" by typing in "2x - 5."
2) If the function is defined implicitly such as 2x - 3y = 4, enter the entire equation as given.
Examples
Sketch the graphs of the following polynomials:
1) y = -3
2) y = 2x - 5
3) y = -x^2 - 4x + 5
4) y = x^4 - 1
5) y = x^3 - 2x + 1
6) -3x^6 = -y - 4x + 1
Calculator solutions
Use the x^n key to enter exponents.
1) y = -3
Enter: -3
2) y = 2x - 5
Enter: 2x - 5
Enter: 2x - 5
3) y = -x^2 - 4x + 5
Enter: -x^2 - 4x + 5
Enter: -x^2 - 4x + 5
4) y = x^4 - 1
Enter: x^4 - 1
Enter: x^4 - 1
5) y = x^3 - 2x + 1
Enter: x^3 - 2x + 1
Enter: x^3 - 2x + 1
6) -3x^6 = -y - 4x + 1
Enter: -3x^6 = -y - 4x + 1. Tap the x variable key twice to enter y as a variable.
Enter: -3x^6 = -y - 4x + 1. Tap the x variable key twice to enter y as a variable.
To show all of the graphs in one workspace, type one equation per line and tap enter after each one.