Vocabulary Algebra 1. FunctionNot a Function Function A relation that assigns exactly one value in...
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Transcript of Vocabulary Algebra 1. FunctionNot a Function Function A relation that assigns exactly one value in...
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Vocabulary
Algebra 1
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Function Not a Function
FunctionA relation that assigns exactly one value in the range to each value of the domain.
Earned income is a function of the number of hours worked. If you earn $4.50/h, then your income is expressed by the function f(h) = 4.5h.
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Independent quantity
A variable that provides the input values of a function.
x y1 32 63 9
In the equation y = 3x, x is the independent variable.
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Dependent quantity
A variable that provides the output values of a function.
x y1 32 63 9
In the equation y = 3x, the value of y depends upon the value of x.
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DomainThe possible values for the input, or the independent variable, of a function.
x f(x)-5 180 22
10.5 32.5
In the function f(x) = x + 22, the domain is all real numbers.
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RangeThe possible values for the output, or dependent variable, of a function.
x y-5 250 07 49
In the function y = x2, the range is the set of all nonnegative numbers.
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Continuous
Data where numbers between any two data values have meaning.
Temperature, length, or weight
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Discrete Data that involve a count of items.
Number of people or number of cars
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Intercepts (x- and y-)
The x- or y- coordinate of the point where a line crosses the x- or y- axis.
The x-intercept of 3x + 4y = 12 is 4. The y-intercept of y = 5x + 2 is 2.
y-intercept
x-intercept
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Linear Non-linear
LinearAn equation or function whose graph forms a straight line.
The graph of y = 2x + 5 is linear.The graph of y = x2 – 3 is not linear.
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Parent function
A family of functions is a group of functions with common characteristics. A parent function is the simplest function with these characteristics.
The linear parent function is y = x.The quadratic parent function is y = x2.
Linear Parent Function
Quadratic Parent Function
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SlopeThe ratio of the vertical change to the horizontal change.
The slope of the line graphed is 1
2 yx
xy
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Slope-intercept form
A linear equation of a nonvertical line written as y = mx + b, where m is the slope and b is the y- intercept.
In the equation y = 3x + 2, the slope of the graph of the line is 3 and the y-intercept is 2.
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-3 -2 -1 0 1 2 3
InequalityA mathematical sentence that compares the values of two expressions using an inequality symbol.
x > 1
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System of equations
Two or more equations using the same variables.
1
21
22
y x
y x
The graph represents the system
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Factor (polynomials)
A factor of polynomial P(x) is any polynomial which divides evenly into P(x). The factorization of a polynomial is its representation as a product its factors. www.mathwords.com
x2 – 4 = (x – 2)(x + 2)
For example, x + 2 is a factor of the polynomial x2 – 4.For example, the factorization of x2 – 4 is (x – 2)(x + 2).
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Parameter changes
The resulting graph of a function when the function’s parameters are changed.
The graph shows the function f(x) = x2 and f(x) = x2 – 3.The parabola shifted down 3 units.
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Polynomial
A monomial or the sum or difference of two or more monomials. A quotient with a variable in the denominator is not a polynomial.
Not Polynomial
3 22 9x x x
2
24 5x
x
Polynomial 2x2, 3x + 7, 28, and – 7x3 – 2 x2 + 9 are all polynomials.
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Quadraticfunction
A function of the form y = ax2 + bx + c, where a = 0.
The graph of a quadratic function is a parabola, a U-shaped curve that opens up or down.
y = 2x2 + 3x + 1
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2 9 0
( 3)( 3) 0
3 0 3 0
3 3
x
x x
x or x
x or x
Quadraticequation
An equation you can write in the standard form ax2 + bx + c = 0.
A quadratic equation can have two, one or no real solutions.
2 0 ax bx c
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VertexThe highest or lowest point on a parabola. The axes of symmetry intersects the parabola at the vertex
The vertex of the parabola is located at (0 , – 4)
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Zeroes (solutions)
The x-intercepts of the graph of a function.
The zeroes of the function are (-3 , 0) and (3 , 0).