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## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 11

Lesson 29: Graphs of exponential functions (Algebra 2 level)

# Transforming exponential graphs (example 2)

Given the graph of y=2หฃ, Sal graphs y=(-1)2หฃโบ³+4, which is a vertical reflection and a shift of y=2หฃ.

## Want to join the conversation?

• what is the difference between Geometric sequence equation and Exponential equation.
• Although both multiply by a common ratio to get to the next number, there are still some subtle differences between them. Geometric sequences are exactly that: sequences. They are a never-ending set of numbers in a list. An exponential equation can only be represented by a graph, and you can't put those values in a list (there are just too many).
• Shall I first learn graphs before getting into this story?
• Yes, start with how to graph points, then graphing linear functions, then graphing quadratic functions. Once you understand those, you should be okay for exponential graphs.
• when Sal says y=2 to the power of x+3, i got confused. How did he get the power of x+3 simplified? What steps did he use?
• Sal had the graph y = 2^x.
The second graph, y = -1 * 2^(x+3) + 4, is a transformation of y = 2^x.
According to March11, Sal must use PEMDAS to track how y = 2^x will transform.
He first works with the exponent (E).
A 3 was added to the x in y = 2^x, making it y = 2^(x+3). Sal transforms the graph accordingly. Afterwards he moves on to the other parts of the transformation (multiplying -1 and adding 4).
There is no simplification involved, only working by chunks.
• In the first graph that Sal made, `y=2^x+3`, at . Why is the y intercept 5? I thought that if x is 0 then 2 would be to the power of 3 which is 8, right? or is it a error?
• As drawn by Sal, the y-intercept is 6. However, you are correct that it should be 8. The difference comes because Sal's drawing is only an approximate sketch. Further on in the video at about , there is a pop-up note that also mentions another inaccuracy of Sal's sketch.
• Is the constant always going to be the horizontal asymptote?
• No, not always.
Consider the rational function f(x) = (ax^n + bx + 6) / (cx^m + dx + 6).
The horizontal asymptote is the horizontal line that f(x) approaches as x approaches positive/negative infinity. You don't have enough information to find that, but you do have enough information to find the y-intercept. What is f(x) when x is zero?

f(0) = 6/6 = 1
y-intercept: (0, 1)

Constants will not be an HA if you're also working with linear equations.
I'm not sure how else constants will be the HA, but it would be a good topic to research.
• i cant understand why in y=2^-x we flipped the graph over the y-axis and in y=-1x2^x+3 we flipped it over x-axis
• How do you determine the y-intercept of an exponential function f(x)= ab^x + k that has been both stretched and translated?
• For any equation, you find the y-intercept by using x=0.
Hope this helps.