![]() So I feel pretty confident with my none of the above. The 1/3 diminishes that, which we see right over there. Use the relevant rules to make the correct transformations. Find the vertical stretch or compression by multiplying the function f(x) by the given factor and the horizontal stretch or compression by multiplying the independent variable x by the reciprocal of the given factor. X would just flipped over, and then multiplying it by Transformation: Vertical or Horizontal Stretch / Compression. So once again, this is negative 1/3 times this right over here. The general form of reciprocal functions is y x ( x h) + k, where a, h, and k are real number constants. As we can see from the three examples, all functions have numerator constants and denominators containing polynomials. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. ![]() ![]() So we get for that point right over there, we get g of negative one Here are some examples of reciprocal functions: f ( x) 2 x 2. Notice that the coefficient needed for a horizontal stretch or compression is the reciprocal of the stretch or compression. f of negative one isĮqual to negative three, and it looks like g of one If we look right over here, it looks like f of negative one. We can do that in aĬouple of other places. Seven is negative one, you take the negative 1/3 times that, and you get positive 1/3. So that seems consistent with this, because if f of negative So it looks like g of negative seven is equal to positive 1/3, positive 1/3, if I am just eyeballing it. Like f of negative seven is equal to negative one. Hitting integer values." So for example, right at this point, right over here, it looks See some values where "it looks like we're Once again, not a choice here, but let's actually look at some values. So it would be 1/3 of negative f of x, which would be negative 1/3 f of x. So it looks like it is 1/3 of this line that I just hand drew, Instead of getting to one right over here, we are only getting to 1/3. Interpretation: A vertical stretch pulls the graph. Three right over here, we're getting to one. Vertical Stretching and Compressing Definition: Vertical transformations adjust the y-values of a function. So instead of getting to four, we're getting to a little bit over one. Negative f of x right there, and it looks like for any x value, what g of x is is 1/3 of that. And that is not one of the choices, which makes me extra cautious, but let me just emphasize So g of x is equal toġ/3 of negative f of x or negative 1/3 of f of x. ![]() So my initial guess - and we can verify this little bit - is that this right over here is 1/3 the value of this. You're flipping over the x-axis and now g of x looks like aĭiminished version of that, and if I were to just eyeball it, it looks like it's roughly 1/3 of this. Because whatever f of x would give you, just take the negative of it If this is y is equal toį of x, then this line right over here that I just drew, that would be y is equal If the constant is greater than 1, we get a vertical stretch if the constant is between 0 and 1, we get a vertical compression. That looks like this, and trying my best to eyeball it. For example, if we begin by graphing the. When we multiply the input by 1, we get a reflection about the y -axis. When we multiply the parent function f (x) bx f ( x) b x by 1, we get a reflection about the x -axis. Perfectly over the x-axis, you would get something In addition to shifting, compressing, and stretching a graph, we can also reflect it about the x -axis or the y -axis. So for example, if you were to flip it perfectly over the x-axis, you would get something- you would get something that looks like- and I'm just going to sketch it. If the constant is greater than 1, we get a vertical stretch if the constant is between 0 and 1, we get a vertical compression. One is if you just eyeball it, it looks like if you flipped f of x over the x-axis, it looksĪ little bit like g(x), but g(x) looks like a version of that that's diminished a little bit. When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. What is g of x in terms of f of x? And they gave us some choices here, and I encourage you to pause the video and see if you can figure this out. Y is equal to f of x, and the g of x is a dotted red line. In the new graph, at each time, the airflow is the same as the original function \(V\) was 2 hours later.- So we're told g of x is a transformation of f of x.
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