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68 Cards in this Set
- Front
- Back
- 3rd side (hint)
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equation of a line
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y - y₁ = m ( x - x1 )
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x is what on the graph
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x is right or left
horizontal |
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y is what on the graph
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y is vertical or up and down
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slope of a line is positive if
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line is increasing from left to right
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m =
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slope
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slope of a line =
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y2 - y1 / x2 -x1
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A function is
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a relation in which each element of the domain (x value - independent variable ) is paired with only one element of the range ( y value - dependent variable )
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A relation can be tested to see if it is a function by the vertical line test. Draw a vertical line through any graph, and if it hits an x-value more than once, it is not a function.
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Linear functions take the form of
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f(x) = mx + b
or y = mx + b |
Where m = the slope
b = the y-intercept so f(x) = 4x - 1 the slope is 4/1 (rise over run) and the y-intercept is -1 |
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The distance between two points of a line can be found using the ?
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Distance formula
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d = square root of ( X2 - X1 )2 + ( Y2 -Y1)2
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The mid-point of a line segment can be found using the ?
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Mid-point formula,
x two plus x one squared over two times y two + y one squared over two |
[ ( X2 + X1 )2 /2 * ( Y2 + Y1 ) 2 /2
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The standard form of a linear function is ?
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0 = Ax + By + C
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The slope is m = -A/B
y-intercept is -C/B |
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Compound interest formula
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A(t) = P(1+i/n) nt
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Compond interest formula
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A(t) = amount
P = principle i = interest rate as a decimal t = time in years n = compounds |
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Slope formula
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m = y2-y1/x2-x1
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slope intercept
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y = mx+b
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m =
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m = slope
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y = mx+b
slope intercept |
m = slope
b = y value of the y intercept |
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Rate of change = slope formula
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m = y2-y1/x2-x1
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Rules of slope formula
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1) y on top y values on top
2) ordered pairs on top of one another 3) Subtraction is part of this process 4) can not have a negative in Denominator |
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To find equation of the line use ?
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slope intercept y=mx+b
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x = Independent
y = Dependent |
Dollars depend on time
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k = slope = Rate of change
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y = mx=b
y = kx |
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Total cost functoion
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C(x) = fixed + variable
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Fixed cost are = ?
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Rent, utilities
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Variable cost are = ?
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Supplies, utilities
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Revenue function = ?
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R(x) = # of units sold or produced times the price
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Profit function
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P(x) = Revenues - Cost or
P(x) = R(x) - C(x) |
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Profit function
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P(x) = R(x) - [variable + fixed]
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Quadratic Functions
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f(x) = Ax2 +Bx + C
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Finding vertex
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x value = -B/2A
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Quadradic formula
f(x) = Ax2 + Bx +C |
x = -B plus or minus the square root of B2 -4AC all over 2A
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Quadradic formula solves for
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Axis of symmetry this formula solves for the middle term
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Absolute value is ?
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Absolute value is the distance from the orgin or zero.
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Laws of exponents =
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Xn * Xm = Xn+m
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10 to the 4th =
10 to the 3rd = 10 to the 2nd = 10 to the 1st = 10 to the 0 = 10 to the -1 = 10 to the -2 = |
10 to the 4th =10000
10 to the 3rd = 1000 10 to the 2nd =100 10 to the 1st = 10 10 to the 0 = 1 10 to the -1 = .1 or 1/10 10 to the -2 = 1/100 |
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Negative exponents
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negtive exponents are only about placement
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Supply and Demand
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q = quantity
x = units produced |
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Increase price to ?
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Increase price to increase units procduced
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Equalibrium is the point where
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they meet on the graph ( where supply and demand meet on the graph)
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distance formula
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d = the square root of (X2 - X1)2 + (Y2 - Y1)2
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distance formula = the square root of x 2 subtracted from x squared plus y 2 - y1 squared
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the graph
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the graph of an equation is a drawing that represents all ordered pair that are solutions of the equation
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m = slope
m = rise / run |
m = change in y / change in x
m = y2 - y1 / x2 - x1 |
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y = m x + b
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m = slope
b = y intercept on graph |
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slope-intercept equation
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y = mx+b
where m = slope and (0,b) is the y intercept |
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point-slope equation
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y-y1 = m(x-x1)
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TO be a function
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the function on the graph can only be touched by the vertical line once
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y = mx or f(x) = mx
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On the graph is a straight line through the orgin (0,0) and the point (1,m).
m = slope |
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Negative slope means the line goes down as you move from left to right.
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if m is zero, then we would have a horizontal line, coinciding with the x-axis.
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The bigger M is the more the line will tilt; so a big slope means steeply tilting line.
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Negative slope means the line goes down as you move from left to right.
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Definition; the variable y varies directly as x, if there is some positive constant m, such that y equal mx.
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Definition; the variable y varies directly as x, if there is some positive constant m, such that y equal mx.
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The weight m, in pounds, of an object on the Moon is directly proportional to the weight E of that object on Earth.
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An astronaut who weighs a hundred eighty pounds on Earth will weigh twenty-eight point eight pounds on the Moon.
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So we have capital M the weight on the moon is little m times capital E the weight on the Earth for any object.
M = mE |
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A linear function is given by, y equal mx plus b or f(x) equal mx plus b,
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and has a graph that is the straight line parallel to the graph of y equals mx and crossing the y-axis at the point (zero, b).
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The point (zero, b) is called the y-intercept.
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y equal mx plus b is called the slope-intercept equation of a line.
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Because the graph is a straight line, its slope is m and its y-intercept is b; its vertical intercept.
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So whenever, in fact, you increase x by a certain amount, y will increase by m times that amount.
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y minus y-one equals m times x minus x-one is called the point slope equation of the line.
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The point is (x-one, y-one) and the slope is m.
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The slope of a line containing points (x-one, y-one) and (x-two, y-two) is m equals y-two minus y-one divided by x-two minus x-one,
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which is the change in y divided by the change in x.
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some times this change in y is denoted by delta y and the change in x is denoted by delta x,
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A quadratic function is given by f(x) equal ax squared plus bx plus c, where a is not equal to zero.
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f(x) = ax squared + bx + c
f(x) ax 2rd +bx + c |
The quadratic function because of this quadratic term, the ax squared, then cannot be a straight line. So curved line
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18/x = x-3
get rid of the denominator by multiplying through by the common denominator of all the fractions |
18x/x = x(x-3)
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18 = x (x-3)
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quadradic function
f(x) axsquared + bx + c |
the graph of a quadratic function is a parabola
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it has a vertex of x = - b /2a
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A = P(1 + i ) t or
A = P ( 1+ i/n ) n*t |
A= amount in the end
P = principal i = the % decimal t = time in years compounded n = # of times compounded |
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Difference quotient is ?
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Average Rate of change
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vertical line is ?
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evaluated at
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prime notation
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y` or f ` (x)
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The derivative of y with respect to " x " is the notation
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dy/dx
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If y = f (x) then the derivative of y with respect to x is
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dy/dx = f ` (x)
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to find the output means
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find the y value
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to find the input means
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find the x value
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output = dependent =
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y
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input = independent =
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x
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