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Y-values are dependent on the chosen x-value.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Why does every point on the x-axis have zero after the comma?",{"text":67,"@type":63},"Because points on the x-axis lie on y = 0, so their coordinate pair is (x, 0).",{"name":69,"@type":60,"acceptedAnswer":70},"What makes a relation a function?",{"text":71,"@type":63},"A function is a relation where each domain value (each x-value) relates to exactly one range value (one y-value). 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We have one axis, the horizontal axis, that is also called the x-axis. The other axis, at a right angle to the x-axis, is called the y-axis. We treat this set of axes like a map, in which points can be located. We always do the x-coordinate of the point first, and then the ycoordinate of the point second. If I am plotting the (x , y) coordinate (3,5), we count off from the origin (that crossing of the two axes, which is (0,0) if we plot that point) three units to the right and five units up:  \nThe domain is composed of x-values. These are values that are elements of the x-axis. The easiest way of thinking of the domain is that we are answering the  \nquestion “what x-values work?” In our picture above, the x-value is 3. If we start atthe origin (where the axes cross) and go to the right three units, we are where x = 3 on the x-axis, and we call that point (3,0). I want you to get this early on, that when we talk about domain, we talk about x-values, and we talk about points that are on the x-axis. Every point on the x-axis will have a coordinate pair with zero after the comma. Why the zero after the comma?  \nNotice that I just asked a question, and did not give out the answer. I want you to take this opportunity to think this through. I’ll ask it again…why does every point on the x-axis have zero after the comma in the coordinate point?  \nBack to the coordinate plane; we also know that the range is composed of yvalues. These are called dependent values, because they depend on what the xvalue is.  \nHere is the exercise I want you to do, and do it until it becomes natural and easy:  \nWith a sheet of graph paper, make coordinate axes, with an x-axis and a y-axis, like you see above. Roll a die, and suppose you get a six. Roll again, and suppose you get a two. Write down the point (6,2). Put your finger or pencil tip on the 6 and say “six is the x-value. Six is my domain.” Then count from the origin (where the axes cross) six units to the right, and hold your pencil there.  \nNext, look at the y-value, which is 2. Say “two is my y-value. Two is my range. Two depends on six, and is told by six to go up two units.” Then move your pencil tip up two places, so that it rests on the point (6,2).  \nAs you practice this, you will be gaining skill in not mixing up the relationship between x and y. You probably know that we move left and we move down by using negative numbers:  \nIf all this seems trivial and easy, great; just know that many great people get tripped up by this and switch x and y. Just remember that x comes first, just like in the alphabet.  \nTasks  \nSuppose we have two points on the plane, (−2,5) and (3,7) . I can plot these points, and then draw a straight line from one point to the other:  \nThere is nothing special about these two points; I could have picked anything, both positive or negative, both x or y. As long as both points are not equal in both x and y, they will be two separate points, and a unique line connects the two, as I have shown above. Please notice that, just like x comes before y in the alphabet, the x-coordinate is first in the pair, and the y-coordinate is second.  \nHere are the tasks:  \n1. Using a single die, roll until you have made up two points to plot below. For example, if you rolled a 1, 4, 3, and 6, you could create the coordinate points (1,4) and (3,6). To be extra crafty, throw in a minus sign somewhere.  \na. What is the distance between these two points you created? Hint: remember the Pythagorean Theorem for a right triangle, that for the legs a and b and the hypotenuse c,  \na 2 + b2 = c 2 .  \nb. What is the midpoint between these two points? Hint: Remember that the midpoint will be the average of the two x-values and the average of the two y-values.  \n2. The points (−2, − 2), (−2,2), (2, − 2) and (2,2) are the corners of a square that centers around the origin of the ","cbCaipVElOZhGR8z","https://ap.wps.com/l/cbCaipVElOZhGR8z","pdf",10552579,42,"English","# Chapter One: What Functions Are, and How They Work\n## Coordinate axes and coordinate pairs\n## Domain and range\n## Practice tasks: distance and midpoint\n## Square around the origin and circle inside\n## What is a function?\n## Vertical Line Test","[{\"question\":\"How do you identify domain and range on a coordinate plane?\",\"answer\":\"The domain is composed of x-values on the x-axis, while the range is composed of y-values on the graph. Y-values are dependent on the chosen x-value.\"},{\"question\":\"Why does every point on the x-axis have zero after the comma?\",\"answer\":\"Because points on the x-axis lie on y = 0, so their coordinate pair is (x, 0).\"},{\"question\":\"What makes a relation a function?\",\"answer\":\"A function is a relation where each domain value (each x-value) relates to exactly one range value (one y-value). The Vertical Line Test is used to check this.\"}]","Chapter One - What Functions Are, and How They Work | PDF",1792132709,106]