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# Transforming exponential graphs

CCSS.Math:

## Video transcript

we're told the graph of y equals 2 to the X is shown below alright which of the following is the graph of y equals 2 to the negative X minus 5 so there's two changes here instead of 2 to the X we have 2 to the negative x and then we're not leaving that alone we then subtract 5 so let's take them step by step so let's first think about what y equals 2 to the negative x will look like well any input we now put into it X we're not going to take the negative of it so if I input a 2 it's like taking the opposite of the 2 and then in putting that into 2 to the X and so what we're essentially going to do is flip this graph over the y axis so here we have the point 2 comma 4 over here we're going to have the point negative 2 comma 4 when x is 0 they're going to give us the same value so they're both going to have the same y-intercept and so our graph is going to look like our graph is going to look something like this they're going to be mirror images flipped around the y axis and so it's going to look it's going to look like that that is the graph of y is equal to 2 to the negative x and then we have to worry about the subtracting 5 from it well that's your subtracting 5 from your final y-value so that's going to or you're subtracting 5 to get your Y value now or your Y values going to be 5 lowers I guess the best way to say it so this is going to shift the graph down by 5 so instead of having the y intercept there's going to be 5 lower 1 to 1 the each hash mark is 2 so this is 1 2 3 4 5 it's going to be right over there so shift down by 5 2 4 5 it's going to look like that and in the asymptote instead of the asymptote going towards y equals 0 the asymptote is going to be at Y is equal to negative 5 so the asymptote is going to be y equals negative 5 so it should look something like it should look something like something like what I'm drawing right now so something like something like that so now we can look at which choices so this this should be the graph of y equals 2 to the negative x minus 5 so let's see which of these choices depict that so this first choice actually seems to be spot-on it's exactly what we drew but we could look at the other ones just in case well this is this looks like what did they do over here it looks like they instead of flipping over the y-axis they took they flipped over the x-axis and then they shifted down so that's not right here it looks like they got what we got but then they flipped it over the x-axis and this looks like they flipped it over the y-axis but then they shifted instead of sitting down by five looks like they shifted to the left by five so we should feel pretty good especially because we essentially drew this before even looking at the choice