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How can you tell if a graph is a function?
A graph is a function if every input (x-value) corresponds to only one output (y-value). One way to check for this is to perform the vertical line test: if a vertical line intersects the graph at more than one point, the graph is not a function.
What is the range of the function shown on the graph?
The range of a function is the set of Y values where the equation is true. Example, a line passing through the origin with a slope of 1 that continues towards infinity in both the positive and negative direction will have a range of all real numbers, whereas a parabola opening up with it's vertex on the origin will have a range of All Real Numbers such that Y is greater than or equal to zero.
How do vertical transformations differ from horizontal transformations?
Vertical transformations involve shifting the graph up or down, affecting the y-values, while horizontal transformations involve shifting the graph left or right, affecting the x-values. Vertical transformations are usually represented by adding or subtracting a value outside of the function, while horizontal transformations are represented by adding or subtracting a value inside the function.
How many boxes are there in graph paper?
The number of boxes on graph paper depends on the size and dimensions of the paper. A standard grid paper may have 4 squares per inch, resulting in 16 boxes per square inch. However, larger grid papers may have more boxes.
What kind of graph would you use to show the ages of kids in a class room?
A bar graph or histogram would be suitable to show the distribution of ages of kids in a classroom. Each bar or column would represent a specific age group, making it easy to compare the different age ranges within the class.
How do you graph and evaluate piecewise functions?
Graph each "piece" of the function separately, on the given domain.
How are piecewise functions related to step functions and absolute value functions?
A piecewise function is a function defined by two or more equations. A step functions is a piecewise function defined by a constant value over each part of its domain. You can write absolute value functions and step functions as piecewise functions so they're easier to graph.
The greatest integer function and absolute value function are both examples of functions that can be defined?
piecewise
What is a piecewise function whose graph resembles a set of stair steps?
One such function is [ Y = INT(x) ]. (Y is equal to the greatest integer in ' x ')
What is piecewise smooth function?
f is a piecewise smooth funtion on [a,b] if f and f ' are piecewise continuous on [a,b]
Is a piecewise function one to one?
A piecewise function can be one-to-one, but it is not guaranteed to be. A function is considered one-to-one if each element in the domain maps to a unique element in the range. In the case of a piecewise function, it depends on the specific segments and how they are defined. If each segment of the piecewise function passes the horizontal line test, then the function is one-to-one.
Describe the defining characteristics of piecewise functions?
A piecewise defined function is a function which is defined symbolically using two or more formulas
When finding the derivative of a point on a piecewise function does every function in the piecewise function need to be continuous and approach the same limit?
All differentiable functions need be continuous at least.
Do you connect points for a piecewise function?
yes :D
Which function is used to model overtime pay?
Piecewise <3
What is a piece-wise function?
for a piecewise function, the domain is broken into pieces, with a different rule defining the function for each piece
What does a solid dot mean on a piecewise function represent?
It could represent a point whose coordinates do satisfy the requirements of the function.
