yes
to tell a function u do the vertical line test, making sure you can only hit the graph once, anywhere on the graph
run ur finger down parallel to the y axis
The vertical line test can be used to determine if a graph is a function. If two points in a graph are connected with the help of a vertical line, it is not a function. If it cannot be connected, it is a function.
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.
In vertical transformations every point on a graph is shifted upwards by a fixed number of points. In a horizontal transformation, every point on a graph is shifted along the x-axis a certain number of points.
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.
Oh, dude, there are like a ton of boxes on graph paper. I mean, it totally depends on the size of the paper, right? But typically, there are like a bazillion little squares on there to help you draw your graphs and stuff. So, like, just grab a piece and start counting if you're really curious, or just trust me that there are a whole bunch.
Graph each "piece" of the function separately, on the given domain.
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.
piecewise
One such function is [ Y = INT(x) ]. (Y is equal to the greatest integer in ' x ')
f is a piecewise smooth funtion on [a,b] if f and f ' are piecewise continuous on [a,b]
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.
A piecewise defined function is a function which is defined symbolically using two or more formulas
All differentiable functions need be continuous at least.
yes :D
A piecewise function is defined by multiple sub-functions, each applicable to a specific interval or condition of the independent variable. Its characteristics include distinct segments of the graph, which can have different slopes, shapes, or behaviors, depending on the defined intervals. The function may have discontinuities at the boundaries where the pieces meet, and it can be defined using linear, quadratic, or other types of functions within its segments. Overall, piecewise functions are useful for modeling situations where a rule changes based on the input value.
Piecewise <3
for a piecewise function, the domain is broken into pieces, with a different rule defining the function for each piece