Polynomials Test
What is the formula for transformed points?
(x+h, Ay+k) Where x and y are the parent function points.
What is a polynomial function?
A polynomial function is a function in the form of: https://tinyurl.com/ycedwd5e (standard form) or https://tinyurl.com/y8mludqf (factored form)* *same as quadratic factored form
What is the multiplicity of a zero, root, or x-intercept?
A zero's multiplicity refers to the number of times that is associated factor appears in the polynomial or the exponents of the factors in factored form. Ex: f(x)=(x+2)(x+5)^6 The multiplicity of the first zero would be 1 and the multiplicity of the second would be 6. I don't know that you can find the multiplicity of a zero in standard form so you might have to factor it.
How would you graph a polynomial function?
I would find the x-intercepts by factoring
What is the leading coefficient?
In standard form, it is the coefficient of the term that contains the highest power of the variable or the coefficient of the term that contains the degree. In factored form, you could plug in the y-intercept and solve for the a value or you could take a shortcut and multiply just the last terms together and then set that equal to the y-value of the y intercept and solve for a. (https://tinyurl.com/ybdk86b2)
What is the degree?
In standard form, it is the highest exponent. In factored form, it is the sum of all of the powers of the groups.
What does the leading coefficient determine about the graph of the function?
It determines the end behavior of the graph. If a is negative then the graph is reflected over the x-axis and if it is positive then the graph will stay the same. What this means is: Positive: As x → ∞ y → ∞ Negative: As x → ∞ y → -∞
What does the degree determine about the graph of the function?
The degree tells you what type of graph the function will have. If it is an even degree there will be some variation of a quadratic function. If it is an odd degree then it will be some variation of a cubic function. The direction in which the function opens up will depend on the a-term (leading coefficient) The degree also determines the turning points of a function in that a function will have no more than n-1 turning points where n is the degree.
What does the multiplicity determine about the graph of the function?
The multiplicity determines the behavior of the graph at the x-intercepts. If the multiplicity is 1 then the function crosses the x-axis like a line. If the multiplicity is an even number then the function "bounces off" the x-axis If the multiplicity is an odd number greater than one then the function crosses the x-axis at a point of inflection.
Which side of the fraction does the term go to when you subtract exponents using the Quotient of Powers property.
You subtract the top from the bottom and it goes to the bottom of the fraction. If it is negative in the top of the fraction then you can further simplify it to go the the bottom.
What is the standard form of power functions?
y = a × x^b
