![]() 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 shift, also known as a translation or a slide, is a transformation applied to the graph of a function that does not change the shape or orientation of the graph, only the location of the graph.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. The term is most commonly used for polynomial functions with a degree of at least three.Ī power function is a polynomial of the form f(x)=ax n where a is a real number and n is an integer with n≥1. All other functions of this type are usually compared to the parent function.Ī polynomial is an expression with at least one algebraic term, but which does not indicate division by a variable or contain variables with fractional exponents.Ī polynomial graph is the graph of a polynomial function. As x→∞,f(x)→∞, and as x→−∞,f(x)→−∞.Īs with quadratics and polynomials, the leading coefficient a changes the vertical “ stretching” of power functions.Ī stretch or compression is a function transformation that makes a graph narrower or wider, without translating it horizontally or vertically.Īn odd power function is a polynomial of the form f(x)=ax n where a is a real number and n is an odd integer.Ī parent function is the simplest form of a particular type of function. For odd powers n, the power function goes from the third quadrant to the first quadrant (like the line y=x).For even powers n, the power function f(x)=ax n is U-shaped (like a parabola) and as x→∞,f(x)→∞.The end behavior of a function describes the y−values as x gets very large (x→∞ in symbols) or as x gets very small (x→−∞). Notice that each power function has only one x− and y−intercept, the origin (0, 0). If n is even, then the power function is also called “even,” and if n is odd, then the power function is “odd.” The graphs of the first five power functions are shown below. A power function is a polynomial of the form f(x)=ax n where a is a real number and n is an integer with n≥1. The most simple polynomial is called a power function. All three these functions belong to a larger group of functions called the polynomial functions. ![]() You have already studied many different kinds of functions, for example linear functions, constant functions, and quadratic functions.
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