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38 Cards in this Set
- Front
- Back
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Domain
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The domain of a fuction is the Set A (x)
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Range
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The set of all outputs (y)
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If the root is odd what is the domain and range?
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infinity
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Absolute Function
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Cube Root Function
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average rate of change formula
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f(b)-f(a)/b-a
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difference quotient formula
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f(x+h)-f(x)/(x+h)-x
or f(x+h)-f(x)/h where x=starting point and h=length of interval |
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Definition of a turning point
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a point where a function changes from increasing to decreasing or vice versa
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Parabola vertical shift
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+ a #
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Parabola horizontal shift
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- a #
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A reflection flipping around the x axis for square root function
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- in front of function
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a reflection flipping around the y axis for square root function
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- under square root sign
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standard form of parabola
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ax^2 + bx+ c
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vertex form of parabola
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(x-h)^2+K
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cubed function equation
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(x-h)^3+K
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cubed root function vertex equation
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cube root (x-h) +K (not under cube root sign)
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An even function f(-x)=f(x)
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reflection around y-axis
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if f(-x)=-f(x) it is an odd function
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rotates 180 degrees around the origin
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How do you know if a function is even?
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if the exponents are all even
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How do you know if a function is odd?
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if all exponents are odd
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how do you test for a 1-1 function?
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f(b)=f(a)
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How do you find the inverse of a function?
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Swap x with the y variable and solve for y
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slope equation
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y2-y1/x2-x1
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How do you find the equation of a line when you have the points the inverse passes through?
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Switch coordinates, the slope is the reciprocal
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marginal cost
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the cost of producting one more item and the slope in a linear cost function
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How do you tell if a parabola opens up or down?
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a function of x: if a>0 it opens up and if a<0 it opens down
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define a quadratic function
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ax^2+bx+c
always represents a parabola |
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How do you tell if a parabola opens left or right?
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if it is a function of y: a>0 it opens to the right if a<0 it opens to the left
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quadratic formula
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vertex formula of a quadratic function
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(-b/2a),4ac-b^2/4a)
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What are the properties of all polynomial and power functions?
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1. continuous domain, no holes
2. No corners or cusps 3.Domain is always (- infinity, infinity) |
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rational function equation
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g(x)/h(x)
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vertical asymptote
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represents a hole in the domain (these lines can never be crossed)
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horizontal asymptote
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represents the end behavior of a direction and these lines can be crossed
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when given a rational function and n>m (n=top exponent, m=lower exponent)
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no horizontal asymptote
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when given a rational function and n<m (n=top exponent, m=lower exponent)
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HA, y=0
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when given a rational function and n=m (n=top exponent, m=lower exponent)
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then y=a^n/b^m
ex: 6x^3/2x^3=3 |
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how do you check if the ha is crossed?
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plug in the HA for the y value and solve, equation must be equal on both sides
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