Apex learning Study Guid Mrs Basama – Flashcards
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Adding Functions
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(f+g)(x)= f(x)+g(x)
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Subtracting Functions
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(f-g)(x)=f(x)-g(x)
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Multiplying Funtions
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(fg)(x)=f(x)•g(x)
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Dividing Functions
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(f/g)(x)=(f(x))/(g(x)), where g(x)≠0
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Composite functions
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(f○g)(x)=(f(g(x)) Domain of (f○g)(x) is all values of x in the domain of g such that g(x) is in the domain of f.
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Horizontal-line test
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If any horizontal line passes through more than one point on the graph of a relation, the inverse relation is not a function.
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Identifying inverse
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If f(g(x))=g(f(x))=x, then f(x) and g(x) are inverse functions.
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Linear Functions
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f(x)=x Constant first differences between y-values for evenly spaced x-values.
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Quadratic Functions
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f(x)=x² Constant first differences between y-values for evenly spaces x-values.
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Exponential Functions
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f(x)=b^x, b>0 Constant ratios between y-values for evenly spaced x-values
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Square Root Functions
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f(x)= √x Constant second differences between x-values for for evenly spaces y-values.
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Midpoint Formula
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[(x₁+x₂)/2, (y₁+y₂)/2]
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Distance Formula
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d = √[( x₂ - x₁) + (y₂ - y₁)]
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Equation of a circle
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(x-h)²+(y-k)²=r²
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Constant sum of an ellipse
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d=PF1 + PF2
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Standard Form Equation of an Ellipse (Horizontal) center at (h,k)
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Equation: ((x-h)²/a²) + ((y-k)²/b²)=1 Vertices: (h+a, k), (h-a, k) Foci:(h+c, k), (h-c, k) Co-vertices: (h, k+b), (h, k-b) c²=a²-b² (major axis length: 2a Minor axis length: 2b)
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Standard Form Equation of an Ellipse (Vertical) center at (h,k)
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Equation: ((y-k)²/a²) + ((x-h)²/b²) = 1 Vertices: (h, k+a), (h, k-a) Foci: (h, k+c), (h, k-c) Co-Vertices: (h+b, k), (h-b, k) c²=a²-b² (major axis length: 2a Minor axis length: 2b)
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Standard Form Equation of a Hyperbola (Horizontal) center at (h,k)
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Equation: ((x-h)²/a²) - ((y-k)²/b²)=1 Vertices: (h+a, k), (h-a, k) Foci:(h+c, k), (h-c, k) Co-vertices: (h, k+b), (h, k-b) Asymptotes: y-k=±b/a(x-h) c²=a²+b² (transverse axis: 2a, conjugate axis: 2b)
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Standard Form Equation of a Hyperbola (vertical) center at (h,k)
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Equation: ((y-k)²/a²) - ((x-h)²/b²)=1 Vertices: (h, k+a), (h, k-a) Foci: (h, k+c), (h, k-c) Co-Vertices: (h+b, k), (h-b, k) Asymptotes: y-k=±a/b(x-h) c²=a²+b² (transverse axis: 2a, conjugate axis: 2b)
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Standard form equation of a parabola (horizontal) vertex at (h,k)
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Equation: x-h=1/4p(y-k)² Direction: Opens right if p>0, Opens left if p<0 focus: (h+p, k) directrix: x=h-p axis of symmetry: y=k
