Ex 4: Let and transform it to where. What would happen? g(x) , so . It looks like this translated (moved) the function up by ten, which is true. However, there is a better way to think about this. Notice that an input of 0 in now looks like an input of 5 in In other f(x+5) f(x). words, what was an input of five is now an input of zero. So, a better way to think about this is that it translated the function five units to the left. Ex 5: Let and transform it to where. What would happen? g(x) , so The output of the transformed function will be three times as big as the original function. This is a dilation transformation. We basically have stretched the graph away from the Note that the x-axis. stayed in place, but the changed. Since the value of the function at the is zero, y-intercept x-intercept zero times anything is still zero. So that point doesn’t move.
Ex 4: Let and transform it to g(x) where. What would happen? , so . It looks like this translated (moved) the function up by ten, which is true. However, there is a better way to think about this. Notice that an input of 0 in f(x+5) now looks like an input of 5 in f(x). In other words, what was an input of five is now an input of zero. So, a better way to think about this is that it translated the function five units to the left. Ex 5: Let and transform it to g(x) where. What would happen? , so The output of the transformed function will be three times as big as the original function. This is a dilation transformation. We basically have stretched the graph away from the x-axis. Note that the stayed in place, but the y-intercept changed. Since the value of the function at the x-intercept is zero, zero times anything is still zero. So that point doesn’t move.
resource_11368.docx