True
Yes, relations can pass the vertical line test if they are functions. The vertical line test states that if a vertical line intersects a graph at more than one point, the relation represented by the graph is not a function. Therefore, for a relation to pass the vertical line test, each input (or x-value) must correspond to exactly one output (or y-value). If it meets this criterion, it can be classified as a function.
The graph must be a straight line, and it must pass through the origin.
Of the three functions, all three pass the vertical line test. That is, if you draw a vertical line anywhere on the graph that the function is, that line will only pass through the function once. All three are also invertible functions, which means that there is a function that is capable of "undoing" the original function. And because the functions all pass the vertical line test, they are all able to be differentiated.
f(x) = -x2 is a function. The equation is solved with just f(x) on one side, and if you were to graph it, it would pass the vertical line test.
No, the graph of an oval/ellipse is not a function because it does not pass the vertical line test.
True
The graph must be a straight line, and it must pass through the origin.
The graph must be linear and pass thru the origin
False
A one-to-one graph must pass both the horizontal and the vertical line test. That means that no x-value can have two y-values and no y-value can have two x-values. An example of a one-to-one function is a line. Things like parabolas and the graph of an absolute function cannot be one-to-one.
Use the vertical line test...pass a vertical line from left to right across the graph. If you hit the graph more than once at a time, there is x-sharing, and it is not a function.
Assuming both the scales on the graph are linear (that is to say that the numbers go up evenly) then YES, a graph which shows direct proportion must be a straight line. It must also pass through the origin (0,0). A straight line which does not pass through the origin is NOT showing direct proportion. Duncan
"y = f(x) is a function if it passes the vertical line test. It is a 1-1 function if it passes both the vertical line test and the horizontal line test. " - In order to be a one-to-one function, it first has to BE a function and pass the vertical line test. For example, a relation on a graph like a circle that does not pass the vertical line test is not function nor one-to-one.
Of the three functions, all three pass the vertical line test. That is, if you draw a vertical line anywhere on the graph that the function is, that line will only pass through the function once. All three are also invertible functions, which means that there is a function that is capable of "undoing" the original function. And because the functions all pass the vertical line test, they are all able to be differentiated.
f(x) = -x2 is a function. The equation is solved with just f(x) on one side, and if you were to graph it, it would pass the vertical line test.
If a proportional relationship is graphed on the coordinate plane, what things must be true?