![]() ![]() Something about the x-axis? Well, we saw it in the example just now. Negative x about the x-axis, it looks like I'm going to get to g. Were to take the reflection of f of negative x, f of Now, that doesn't quite get us to g, but it gets us a little bit closer 'cause it looks like if I So when you input six into it, that would be f of It'd have the straight portion like this. Here, in order to get g? So f of negative x would be a reflection of f about the y-axis. How do we transform f of x, actually, they've labeled it over here, this is f of x right over ![]() What is the equation of g in terms of f? So pause this video and ![]() We're told functions f, so that's in solid in this blue color, and g dashed, so that's right You'd pick the choice that would actually look like that. So g of x is going to look something like that, a reflection about the x-axis. And so g of x would beĪ reflection of f of x about the x-axis. You could see that whateverį of a certain value is, g of that value wouldīe the negative of that. So it's going to be equal to negative two. So one way to think about it is we can see that f of zero is two, but g of zero is going toīe the negative of that. So instead of it being f of negative x, it's equal to the negative of f of x. X is equal to, notice, all of this right over here, that was our definition of f of x. All right, so in this situation, they didn't replace the x And then they say what is the graph of g? And so pause this video and at least try to sketch it out in your And if you're doing this on Khan Academy, you'd pick the choice So g is going to look something like this. And we've already talkedĪbout it in previous videos that if you replace your Same thing as f of zero 'cause a negative zero is zero. What would g of zero be? Well, that would be the Same thing as f of two, which is zero, so it What would g of negative two be? Well, that would be the G of negative four is going to be equal to f of the negative of negative four, which is equal to f of four. Negative four to be equal to two because, once again, g of negative four, we could write it over here. That f of four is equal to two, so we would expect g of ![]() So whatever the value ofį is at a certain value, we would expect g to take on that value at the negative of that. Over that g of x is equal to f of negative x. Try to think about it, at least in your head. What g would look like without having any choices, What is the graph of g? And on Khan Academy, it's multiple choice, but I thought for the sake of this video, it'd be fun to think about Of exercises on Khan Academy that deal with reflections of functions. Transformations are used to change the graph of a parent function into the graph of a more complex function.Going to do in this video is do some practice examples Stretching a graph means to make the graph narrower or wider. They are caused by differing signs between parent and child functions.Ī stretch or compression is a function transformation that makes a graph narrower or wider. Reflections are transformations that result in a "mirror image" of a parent function. Reflecting a graph means to transform the graph in order to produce a "mirror image" of the original graph by flipping it across a line. All other functions of this type are usually compared to the parent function. Sketch the graph of each of the following transformations of y = xĪ stretch or compression is a function transformation that makes a graph narrower or wider, without translating it horizontally or vertically.įunction families are groups of functions with similarities that make them easier to graph when you are familiar with the parent function, the most basic example of the form.Ī parent function is the simplest form of a particular type of function. Graph each of the following transformations of y=f(x). Let y=f(x) be the function defined by the line segment connecting the points (-1, 4) and (2, 5). ![]()
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