Now, graphing those on the same axes, we have: Now for f(− x)į( −x) = −3 x + 2 (replace every ' x' with a ' −x'). What we've done is to take every y-value and turn them upside down (this is the effect of the minus out the front). Note that if you reflect the blue graph ( y = 3 x + 2) in the x-axis, you get the green graph ( y = −3 x − 2) (as shown by the red arrows). When you graph the 2 lines on the same axes, it looks like this: Our new line has negative slope (it goes down as you scan from left to right) and goes through −2 on the y-axis. going uphill as we go left to right) and y-intercept 2. You'll see it is a straight line, slope 3 (which is positive, i.e. If you are not sure what it looks like, you can graph it using this graphing facility.
Let's see what this means via an example. This mail came in from reader Stuart recently:Ĭan you explain the principles of a graph involving y = − f( x) being a reflection of the graph y = f( x) in the x-axis and the graph of y = f(− x) a reflection of the graph y = f( x) in the y-axis?
