When both axis' are increasing it is a positive correlation.
When both are decreasing it is a negative correlation.
When the dots are all over the place then there is no correlation.
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A line graph.
the line of symmetry would occur at x=0
All of the algebraic transformations occur after the function does its job, all of the rules from the two charts above to transform the graph of a function.
When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.
The "x values that work are the domain numbers like for y=x+1 would be any real number. But, y= sqrx x would have to be non-negative.