Horizontal compression example12/20/2023 ![]() ![]() X would just flipped over, and then multiplying it by ![]() So once again, this is negative 1/3 times this right over here. So we get for that point right over there, we get g of negative one 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. Three right over here, we're getting to one. 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 That looks like this, and trying my best to eyeball it. Perfectly over the x-axis, you would get something 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. 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. 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. A function presented in tabular form can also be reflected by multiplying the values in the input and output rows or columns accordingly.- So we're told g of x is a transformation of f of x.The order in which the reflections are applied does not affect the final graph. A graph can be reflected both vertically and horizontally.A graph can be reflected horizontally by multiplying the input by –1. We input a value that is 3 larger for g\left(x\right) because the function takes 3 away before evaluating the function f. To get the same output from the function g, we will need an input value that is 3 larger. For example, we know that f\left(2\right)=1. The formula f\left(x\right)=f\left(x - 3\right) tells us that the output values of g are the same as the output value of f when the input value is 3 less than the original value. ![]()
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