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20 Cards in this Set
- Front
- Back
Describe key points of Graphical Representation
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1. Any point in a graph is located by two co-ordinates.
2. First coordinate is (3,2) is the X-value (horizontal); the second is the Y value (vertical) |
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What is the Origin in graphs?
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Fixed point on the graph representing the coordinates (0, 0)
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What is a quadrant?
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One of the 4 sections that a graph is split into. Each quadrant has different signs for the x and y values.
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Define a Linear function
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Function that results in a straight line. X and Y are not raised to powers. No exponents, logarithms, etc.
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Shape of Squared function.
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"U" shaped
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Shape of cubed function.
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"Z" on its side
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Describe parts of linear function:
y = mx + c. |
m - coefficient of x, also slope (gradient) of the line.
C is the y intercept |
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Formula for slope
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(y1 - y2) / (x1 - x2)
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Three possibilities for m (slope).
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m is negative. Line leans in backward direction.
m is zero. then y - constant. Line is parallel to the x axis x = constant, is parallel to the y axis. Slope is infinite. |
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Equation of straight line can be determined if the values for m and c are known. Can determine if what info is available.
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1. Values of m and c
2. Value of m and 1 set of coordinates 3. Value of c and 1 set of coordinates 4. Coordinates of 2 points on line |
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Explain solving of two linear equations in two variables.
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Finding a point which satisfies both equations. 1 of 3 outcomes:
1. One common point. Unique solution. 2. Infinite number of solutions. Same line. 3. No solution, equations are inconsistent. Runs parallel to each other. |
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What are exponential functions important?
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The way they express growth or decay. Natural pattern of both.
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What is the difference between linear and exponential growth.
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Linear is growth by a constant increase
Exponential represents a constant percentage increase. |
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Basic logarithmic equation
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if y = a to the xth , then x is said to be the logarithm of y to the base a.
log a y = x. |
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What is a common logarithm?
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Logarithms to the base 10
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What is a binary logarithm?
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Logarithms to the base 2.
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What is a natural logarithm?
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Logarithms to the base e.
Written x = ln y means x = log e y. |
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Rules for logarithms?
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1. Addition: log a x + log a y = log a xy.
2. Subtraction: log a x - log a y = log a x/y 3. Multiplication by a constant: c log a y = log a y to the cth. |
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General form of exponential function:
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y = ka to the cxth.
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Transformation
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by taking logarithms of both sides of a exponential function can be treated as a linear one.
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