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Chapter 2 Precalculus Review
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Sections 2.1-2.8
Terms in this set (36)
Leading Coefficient
The number in front of the X of the highest degree
(ex.) (4)x^2
Degree
The highest exponent in a polynomial determining the number of zeros
Zero Function
A polynomial with no degree and a slop of zero
{f(x)= 0 }
Constant Function
A polynomial with a constant and no degree
{f(x)= a}
Linear Function
A polynomial with a degree of 1
{f(x)= ax^2 +b}
Quadratic Function
A polynomial with a degree of 2; in standard form and often FOILed
{f(x)= ax^2 + bx + c }
Correlation Coefficient
A number indicating the strength/weakness, and positivity/negativity of a scatter plot
**closer to 1/-1; stronger correlation
**closer to 0; weaker correlation
Axis of Symmetry
Line marking the perfect reflection of the graph within a parabola
Vertex
Highest/Lowest point of a graph; point where the parabola and the axis of symmetry intersect
Quadratic Formula
X equals -b, plus/minus the square root of B squared - 4AC; divided by 2A
Standard Quadratic Form
f(x)= ax^2 + bx +c
Vertex Form
f(x)= a(x-h)^2 + k
Intercept Form
f(x)= a(x-p)(x-q)
Power Function
Any function that can be written as f(x)= k * x^a, or with an x raised to a power
Linear Power Function
f(x)= x
Quadratic Power Function
f(x)= x^2
Cubic Power Function
f(x)= x^3
Reciprocal power Function
f(x)= x^-1 or 1/x
Square Root Power Function
f(x)= x^1/2
multiplicity
Amount of times a factor is multiplied; the exponent referring to the number
Remainder Theorem
If a polynomial f(x) is divided by x-k, the remainder is r=f(k)
Factor Theorem
A polynomial f(x) has a factor x - k if and only if f(k) = 0
synthetic division
a method used to divide a polynomial by a binomial, a shortcut for long division
Rational Zeros Theorem
Finding the rational (not irrational) zeros of a polynomial function; compare the factors of the constant over the factors of the leading coefficient
Upper Bound
Any positive value above or on the x axis
Lower Bound
Any negative value below or on the x axis
Fundamental Theorem of Algebra
A polynomial will have as many roots as its degree (both real and imaginary)
Linear factorization theorem
if f(x) is a polynomial of degree n where n>0, f has precisely n linear factors
Complex Conjugate Zeros Theorem
If (a + bi) is a factor of f(x), then (a - bi) is also a factor
Rational/Reciprocal Function
f(x)= g(x)/r(x); the denominator cannot equal zero
End Behavior Asymptote
-If the degree of the denominator > the degree of the numerator, the end behavior. asymptote=horizontal asymptote y=0
-If the degrees are equal, then the end behavior asymptote is the quotient of the leading coefficients
-If the degree of the numerator > the degree of the denominator, then there is no horizontal asymptote
Vertical Asymptotes
Determined by setting the denominator = to zero, x= V.A.
x intercept
Determined by setting the numerator equal to zero, the point where the line crosses the x axis the value for x when y=0
y intercept
Determined by dividing two zeros; the point where the line crosses the y axis the value for y when x=0
-ex; f(x)= (x-a)/(x-b) -> (-a/-b)
extraneous solutions
results that are not solutions to, or cannot satisfy the original equation
sign chart
used to determine on which intervals a polynomial function is positive or negative, shows x-axis as a number line and the zeros as numbers on the line
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