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For a graph to be a function, each x-value has to take maximum one y-value. One way you can check this is drawing a vertical lines through points on the graph. If a single vertical line intersects the graph in more than one place, that means the x-value defining the line has more than one y-value, and the graph is not a function.
tl;dr: Draw vertical lines through the function, and if the lines only intersect the graph once, you have a function.
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How does you know that relation is a function?
One way is to try the vertical line test on a graph!
What is the name of a graph shaped a bit like a y-x2 parabola but on the way up its steeper than on the way down?
The cubic function is the name of graph that is steeper on the way up than on the way down. An absolute value function is a grpah that is shaped a bit like a y=x2 parabola.
When is a relation considered to be function?
A relation is a function when an x value only has one y value associated with it. An easy way to tell this is to graph the relation, then draw a vertical line through it. If, at any point, it touches the graph twice, the relation isn't a function.
Is the relation a function y equals 3x-4?
7
How to sketch the grap of the function y -2x 2-4x-6?
The best way to sketch a graph of the function y -2x 2-4x-6 is to first get the values of Y and X and then use the values to sketch the graph.
Does a derivative exist if the graph goes through the origin?
It may or may not exist. Whether or not the graph goes through the origin does not in any way affect whether or not it has a derivative. A function has a derivative if it has no discontinuities, cusps, sharp corners, or vertical tangents.
Can you determine whether the inverse of a function is a function by using vertical line test?
Not quite. You can use a vertical line test on the graph of the inverse mapping, OR you can use a horizontal line test on the original graph. The horizontal line test is used in the same way.
Is there a way to demonstrate that the problem of determining whether a given path exists in a graph is NP-complete?
Yes, the problem of determining whether a given path exists in a graph can be demonstrated as NP-complete by reducing it to a known NP-complete problem, such as the Hamiltonian path problem. This reduction shows that the path existence problem is at least as hard as the known NP-complete problem, making it NP-complete as well.
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.
How does you know that relation is a function?
One way is to try the vertical line test on a graph!
Is the problem of determining whether a given graph can be colored with 3 colors in such a way that no two adjacent vertices have the same color, known as the 3-coloring problem, considered to be NP-complete?
Yes, the 3-coloring problem is considered to be NP-complete.
What is the name of a graph shaped a bit like a y-x2 parabola but on the way up its steeper than on the way down?
The cubic function is the name of graph that is steeper on the way up than on the way down. An absolute value function is a grpah that is shaped a bit like a y=x2 parabola.
When is a relation considered to be function?
A relation is a function when an x value only has one y value associated with it. An easy way to tell this is to graph the relation, then draw a vertical line through it. If, at any point, it touches the graph twice, the relation isn't a function.
Stephen Douglas promoted what as a way of determining whether a state should be slave or free?
popular sovereignty
You are told that the average rate of change of a particular function is always negative What can you conclude about the graph of that function and why?
It is a function whose graph starts in the top left and goes to the bottom right. There could be some intervals in which the graph moves upwards to the right. This follows from the definition of average rate of change.
Is the relation a function y equals 3x-4?
7
How to sketch the grap of the function y -2x 2-4x-6?
The best way to sketch a graph of the function y -2x 2-4x-6 is to first get the values of Y and X and then use the values to sketch the graph.
