Functions on a Cartesian Plane
Key Questions
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Answer:
There is a procedure to graph a function.
Explanation:
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Define the domain and codomain
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Find the intersection between function and x-axes:
solve#f(x)=0# -
Calculate the first derivative and its intersection with x-axes:
#f'(x)=0# . This points are called extrema, geometrically represent the points where the tangent of the function is horizontal. This mean that the function reach its minimum or maximum or stationary points. -
Calculate the second derivative and its intersection with x-axes:
#f''(x)=0# . This points (inflection point) are points on a curve at which the curve changes from being concave to convex or vice versa.
if#f''(x)>0 # the function is convex (is smiling)
if#f''(x)<0 # the function is concave (is sad)
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Answer:
See explanation below
Explanation:
#(x,y)# is a pair of real numbers. The meaning is:#(x,y)# is an ordered pair of numbers belonging to#RRxxRR=RR^2# . The first pair memeber belongs to the first set#RR# and the second belongs to second#RR# . Althoug in this case is the same set#RR# . Could be in other cases#RRxxZZ# or#QQxxRR# #(x,y)# has the meaning of an aplication from#RR# to#RR# in which to every element x, the aplication asingns the y element.#(x,y)# has the meaning of plane's point coordinates. The first x is the horizontal coodinate (abscisa) and second is the vertical coordinate (ordenate). Both are coordinates.#(x,y)# has the meaning of a complex number: x is the real part and y is the imaginary part:#x+yi# #(x,y)# has the meaning of a plane's vector from origin of coordinatesetc...
You will see that meaning of
#(x,y)# could be whatever of above depending of context, but if you think a little bit, all meanings are quite similarHope this helps
Questions
Expressions, Equations, and Functions
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Variable Expressions
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Expressions with One or More Variables
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PEMDAS
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Algebra Expressions with Fraction Bars
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Patterns and Expressions
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Words that Describe Patterns
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Equations that Describe Patterns
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Inequalities that Describe Patterns
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Function Notation
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Domain and Range of a Function
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Functions that Describe Situations
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Functions on a Cartesian Plane
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Vertical Line Test
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Problem-Solving Models
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Trends in Data