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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.
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.
Stephen Douglas promoted what as a way of determining whether a state should be slave or free?
popular sovereignty
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.
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.
How do you make a graph of a quadratic function that has x-intercepts at 0 and 4?
That's not enough information to draw the graph. All you know is that it crosses the x-axis at those 2 points. You don't know whether it opens upward or downward, or how far the nose is above or below the x-axis. You need more information about the function before you can graph it. This is just another way of saying that there are an infinite number of different quadratic functions that all have those same x-intercepts.
What term is used to describe a represntation of a thing or system and can be used as a way to test hypotheses?
A graph is a representation of a thing/system, and can be used to test a hypothesis. For example, if you have a graph of a trend you can find the function of that trend. Then, you can plug in values the graph defines--say, at 2 the graph reaches 5--and if the function works, you know you have modeled the phenomenon correctly. This function testing can work to test a hypothesis, especially in finding trends.
How will you determine if a graph is a function or a mere relation?
You use the "vertical line test". If anywhere you can draw a vertical line that goes through two points of the graph, the relation is not a function; otherwise, it is a function. This is just another way of saying that in a function for every x value (input) there is AT MOST one y value (output).
