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### Course: Algebra 2>Unit 9

Lesson 7: Graphs of exponential functions

# Transforming exponential graphs

Given the graph of y=2ˣ, Sal graphs y=2⁻ˣ-5, which is a horizontal reflection and shift of y=2ˣ.

## Want to join the conversation?

• I'm a bit confused here..because 2^2=4 yes BUT 2^-2=1/4 Or perhaps I'm just not understanding this problem fully.. Please help out.
• What you just said, is what Sal graphed!

With a x value of -2, the y value becomes 4.
2^-(-2) = 2^(2) = 4
hence the coordinate, (-2, 4)

With a x value of 2, the y value is 1/4, or 0.25.
2^-(2) = 2^-2 = 1/4
the coordinate is (2, 1/4).
• Anyone have any idea about what "asymptote" means at ?
• An asymptote is an 'imaginary' line, that the curve/function approaches but never touches (nor intersect).
• How did Sal know that -5 was going to be the horizontal asymptote, why not the vertical one?
• Because we know the graph of y=2^x has a horizontal asymptote as y=0
The graph y=2^(-x) reflects y=2^x over the y-axis
y=2^(-x)-5, the -5 is the vertical shift, so it moves the graph 5 units down. Essentially, it moves the horizontal asymptote 5 units down as well.
• I think the explanation isn't very helpful here... At , Sal says "Any input we now put into x, we now take the negative of it, so if I input a 2, it's like taking the opposite of the 2 and then inputting that into 2^x." - and then he immediately goes "So it's like we're flipping the graph over the y-axis."

I feel like that's quite a mental jump that isn't at all immediately intuitive to me (and it appears others as well, judging from the comments).

2^(-2) = 1/4 and if we set y to 4, we get this at 4 = 2^-(-2) = 2^(2).

So while I can see numerically that we're flipping the graph horizontally, Sal's explanation isn't intuitive to me at all here, and seems to be making too big a leap.
• why is not the value of y = 1/4 ,since the exponent is = -2
• Could you please specify a time stamp or reference point in the video? Sal is working with multiple different functions and graphs. All involve 2^x or 2^(-x). So, it is unclear what you are referring to.
• Is mathematics 3 a high school level or university ?
(1 vote)
• Mathematics 3 is high school level mathematics.
In most universities they would expect that you understand most of the topics in that section.
• How can i do this algebraically?
• What is the Asymptote?
(1 vote)
• A function's asymptote is a straight line that a curve approaches as it moves towards infinity. The function will never touch that asymptote. In the case of y=2^x, think of it algebraically. Any power you raise 2 to will never be zero or negative. That is why when you graph it, y can be infinitely small as you decrease x (because 2^ a negative number will have infinitely small fractions), but it will never touch the asymptote, which in this case is y=0. However, if you transform a graph, you move the asymptote with it. In the case of something like y=2^x-5, you move the graph down by 5, and since 2^x will never be below or equal to zero, y will never be <= 0-5 = -5. So the new asymptote is y=-5. Hope this helps!