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What are the steps for writing the equation of a function from a graph?
1. Decide if the graph looks like any standard type of graph you've seen before. Is it a type of sine or cosine? A quadratic? A circle or ellipse? A line? An exponential? (You get the idea.) If you can't find a standard type to match your desired graph, pick one that looks close to it and recognize that you will be doing an approximation to your function.2. Once you have an idea of what you're graph should be like, think about the equations that are used to describe that graph. Where do the numbers go and how do they affect how the graph looks/moves/ behaves? Some functions, such as circles, hyperbolas, and quadratics, have standard equations with variables based on the important features of the graph (such as the center, maximums or minimums).3. Find the important and/or interesting parts of the graph and use them in the equation. As stated before, ellipses and such have special equations to describe them. Sines and cosines require the amplitude, frequency, and phase shift.4. Check your equation if you can. It's always good to plug a few of the points that are in your graph to make sure your equation is accurate. It's especially good to try out points you did NOT use to find your equation. If it works for these, then you probably did it right.
Y equals b plus x plus x2?
y=b+x+x^2 This is a quadratic equation. The graph is a parabola. The quadratic equation formula or factoring can be used to solve this.
What is the significance of the slope in the graphs?
This is the first fundemental theorem of Calculus. The slope of a line is very important in your first calculus course. The slope tells you the rate of change. This means how much is the object change in height compared to its change in length. The slope of a line in Calculus is used as the first derivative. If you can take the slope of a line at one particular point you will find the answer to the derivative at this point. Remember this. You first equation on your graph is called your position equation. If you take the derivative of this equation it is called the velocity equation. The velocity equation is how much the position equation is sloping at each point. If you take the derivative of the velocity equation you will get the acceleration equation. The accerelation equation is how much the velocity is sloping at each point. You can take the derivative of the acceleration equation and this will give you the jerk equation. The jerk equation is not used in many applications and I have never used this equation in any of my 4 calculus classes.
Recall that the vertical line test is used to check whether a particular graph represents the graph of a function what are correct statements for this graph?
This graph fails the vertical line test at x = 3This graph is not the graph of a function.
Explain how the graph of fx ln x be used to graph the function gx ex -1?
graph gx is the reflection of graph fx and then transformed 1 unit down
Can a graph be used to determine the number of solutions an equation has?
Yes.
How can a graph be used to determine how many solutions an equation has?
Count the number of many times the graph intersects the x-axis. Each crossing point is a root of the equation.
What is a liner?
An equation used to graph certain numbers.
What is y equals 2x-1?
3
What are the steps for writing the equation of a function from a graph?
1. Decide if the graph looks like any standard type of graph you've seen before. Is it a type of sine or cosine? A quadratic? A circle or ellipse? A line? An exponential? (You get the idea.) If you can't find a standard type to match your desired graph, pick one that looks close to it and recognize that you will be doing an approximation to your function.2. Once you have an idea of what you're graph should be like, think about the equations that are used to describe that graph. Where do the numbers go and how do they affect how the graph looks/moves/ behaves? Some functions, such as circles, hyperbolas, and quadratics, have standard equations with variables based on the important features of the graph (such as the center, maximums or minimums).3. Find the important and/or interesting parts of the graph and use them in the equation. As stated before, ellipses and such have special equations to describe them. Sines and cosines require the amplitude, frequency, and phase shift.4. Check your equation if you can. It's always good to plug a few of the points that are in your graph to make sure your equation is accurate. It's especially good to try out points you did NOT use to find your equation. If it works for these, then you probably did it right.
What type of graph should be used to display percentage data?
a circle graph
Which equation is most likely used to determine the acceleration from a velocity vs. time graph?
The acceleration can be determined from a velocity vs. time graph by finding the slope of the line at a specific point. The equation used to calculate acceleration from a velocity vs. time graph is given by a = Δv/Δt, where a is the acceleration, Δv is the change in velocity, and Δt is the change in time.
What does an arrow in an equation mean?
---------> is yield
What graph should be used with categorical data?
histograph
Which method is used to calculate the slope on a distanced-time graph?
Slope = change in y (distance) / change in x (time). If the graph is not a straight line then either apply the above formula to the tangent at the point of interest or differentiate the equation of the graph.
What kind of graph should be used by comparing the cost of 4 bicycles?
a bar graph would be best I might say
What does graph mean as a mathematical word?
The word graph can be used either as a noun or a verb. As a noun, it means a picture or visualization of some mathematical term or relationship. The most usual type of graph is the Cartesian coordinate system invented by the great French mathematician, René Descartes, but there are several other types. As a verb, to graph is to depict in the form of a graph, as in, graph that equation.
