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Unit 6 Analyzing and Comparing Functions part 1
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Terms in this set (26)
Axis Of Symmetry
A line that a graph can be folded over so that both halves match each other perfectly; Always written as x = ?; when equation is written in vertex form, axis of symmetry is x=h.
Decreasing
A function whose graph goes down (falls) as it is followed from left to right.
Domain
The set of all x-values in a relation; (how far left to right on a graph the function will go).
Exponential function
A function whose equation carries the input variable as its exponent: f(x) = b^x; the graph is L-shaped and has a horizontal asymptote.
Function
In this relationship between two quantities, for each input there is exactly one output.
Increasing
A function whose graph goes up as it is followed from left to right.
Interval
The distance between two values or points.
Linear Function
A function of the form f(x) = mx + b, where m and b are real numbers; the graph is a straight line.
Quadratic Function
A function where the polynomial has a degree of 2. The graph is U-shaped .
Range
The set of y-values that a graph is defined for; (how far up and down on a graph the function will go).
Vertex
The very lowest or highest point of a quadratic or absolute value graph; when equation is written in vertex form, vertex is (h, k).
Zeroes
The x-coordinate where a graph intersects the x-axis; also known as the x-intercept or root of a function. The value of x when the y-coordinate is 0.
Maximum
The x-value where a graph has the highest output; where the graph peaks.
Minimum
The x-value where a graph has the lowest output; where the graph has a valley.
Symmetry
When a line cuts a graph in half such that each half on either side of the line matches exactly.
x-intercept
The point on a graph when y = 0 in an ordered pair; where a line crosses the x-axis; also known as the roots or zeroes of a function.
y-intercept
The point on a graph when x = 0 in an ordered pair; where a line crosses the y-axis.
Piece-wise function
a function that is a combination of one or more functions
step function
a piecewise function that is constant over each interval in its domain; resembles a set of steps
cubic function
a function whose degree is 3; F(x)= x^3
square root function
a function involving the square root of x
absolute value function
a function involving the absolute value of x; the graph is shaped like a 'V'
polynomial function
A function whose expression is the sum of a number of terms; exponents are positive integers; there are no variables in the denominator of any term; graphs are continuous (have no breaks or gaps) with smooth curves (no sharp turns). Equation can also be written as 3 or more factors: f(x) = (x + a)(x + b)(x + c)
Included values
Values that are part of a given or displayed interval; Represented by: closed/colored-in circles; >= or <=; [ a1, a2]
Excluded values
Values that are not part of a given or displayed interval; they simply mark the constraint or boundary of the interval; Represented by: open/blank circles; > or <; ( a1, a2)
Degree of a polynomial
the highest exponent of a polynomial function; tells the MAXIMUM number of roots the function will have (it can have less though)
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