+23246 In the top two graphs, the value of y depends upon the value of x.
The top graph looks close to: y = -|x| + 2 so, as you put in various values for x, you get different values for y.
The middle graph looks like a modification of a y = sin(x) or y = cos(x) graph. Again, as you put in different values for x, you get different values for y.
But, the last one: The only number that you can put in for x is 1.5, but there are an infinite number of y-values that pair with this x-value. Some examples are (1.5,0), (1.5,1), (1.5,-2), (1.5,653434). The value of y does not depend upon the value of x; it can be anything. So, this is not a function. Similarly, it does not pass the vertical line test; the vertical line that passes throught this vertical line hits this line, not in just 1 point, but in an infinite number of points.
Does this help or it is as clear as mud?
+23246 The vertical line test: when looking at a graph, if every vertical line that you can draw will intersect the graph in at most one point, then the graph is the graph of a function.
So, two out of the three are function, but one of them isn't. Can you figure out which are functions?
+277 WAIT THIS IS THE WRONG QUESTION!! THE QUESTION IS
Decide whether the graph represents y as a function of x. Explain your reasoning.
+23246 In the top two graphs, the value of y depends upon the value of x.
The top graph looks close to: y = -|x| + 2 so, as you put in various values for x, you get different values for y.
The middle graph looks like a modification of a y = sin(x) or y = cos(x) graph. Again, as you put in different values for x, you get different values for y.
But, the last one: The only number that you can put in for x is 1.5, but there are an infinite number of y-values that pair with this x-value. Some examples are (1.5,0), (1.5,1), (1.5,-2), (1.5,653434). The value of y does not depend upon the value of x; it can be anything. So, this is not a function. Similarly, it does not pass the vertical line test; the vertical line that passes throught this vertical line hits this line, not in just 1 point, but in an infinite number of points.
Does this help or it is as clear as mud?
