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16 Cards in this Set
- Front
- Back
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Function
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A set of numbers with no repeating x-values. Plug in x to get y. Must pass a vertical line test.
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Even/odd functions
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Plug in -x. If the function changes, it is odd, but if it does NOT, then it is even.
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Symmetry
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Plug in -x. If the function changes, then it is symmetrical about the origin (vertex). Otherwise, it is symmetrical about the y-axis.
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Difference quotient
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[f(x+h)-f(x)]/h
Plug equation into x. Solve. |
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Slope equation
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(Y2-Y1)/(X2-X1)
Can also be used to find the average rate of change. |
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Point slope form
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y-y1=m(x-x1)
m=answer from slope equation |
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Slope intercept form
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y=mx+b
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General form
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Ax+By+c=0
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Standard form of a Quadratic equation
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a(x-h)^2+k
NOTE: (h,k)=(x,y) (h,k)=vertex (solve for) h=shift in x k=shift in y |
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Finding the domain
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Contains no division or square roots=(-infinity,infinity)
Contains division=solve the denominator. Contains square root=solve inside of radical sign. Since only nonnegative numbers have square roots, the domain always moves upward. |
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Inverse of a function
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1. Replace f(x) with y.
2. Interchange x and y. 3. Solve for y. (note: functions with an inverse are "one-to-one" and must pass a vertical line test). |
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Inverse of a point
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Reverse the value. For example, if the point is (a,b), then switch the values to (b,a).
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Distance formula
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√[(x2-x1)^2]+[(y2-y1)^2]
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Midpoint formula
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(x1+x2)/2 , (y1+y2)/2
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Standard form of a circle
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(x-h)^2 + (y-k)^2 = r^2
(h,k)=center of circle r^2= radius squared |
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General form of a circle
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x^2+y^2+Dx+Ey+F=0
To solve: Separate x and y components, complete the square, factor. |
