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### Course: Algebra 1>Unit 12

Lesson 3: Graphs of exponential growth

# Graphs of exponential growth

Identifying which graph represents a given exponential function.

## Want to join the conversation?

• can somebody please tell me what does f(x) mean
• Okay, so you know what "y = 3x + 4" means right?
Well, when we input an x into that equation, we map out a y value. As we get into more advanced math, we will start using "f(x) = 3x + 4" instead of "y = 3x + 4". But they are essentially the same thing; f(x) is a function where if we input any non-restricted x value we will map out a "y" value. Thus "y = f(x)". One convenient use of "f(x)" is that we can use separate equations/functions and not confuse ourselves. e.g.:
f(x) = 3x + 4
g(x) = (1/2)x - 2
If we used y, then we could get confused by whether or not we were talking about the same equation/function. So using function notation removes the confusion there.
Hope this helps,
- Convenient Colleague
• explain to me why a negative power is always a fraction? and Why Sal drew curved lines between the points.
• As an example, going backwards from 2^3 = 8, divide both sides by 2 gives 2^2 = 4, 2^1 = 2, 2^0 = 1. When we keep going, 2^-1=.5 = 1/2, 2^-2 = .25 = 1/4, etc. However, a negative power is not always a fraction, it is a reciprocator. So 1/(2^-2) = 2^2 = 4.
• how do you graph an exponential function with a table??
• You pick values for X and calculate the corresponding Y value just like Sal does in the video.
You should then have a list of ordered pairs (x, y).
Graph them.
• Is it correct that in this example the x-intercept doesn't exist since the graph never touches the x-axis?

Could anyone give me an example of an exponential function which would have an x-intercept if we graphed it?
I'm thinking of something along the lines of f(x)=m*(n^x)-c (though would we still call it an exponential function or is it more like a "combined" sort of thing?), but I'm interested whether there is a bare-bones exponential function of the form f(x)=m*n^x without adding or subtracting anything
• So I have a question my problem is: y=-2(1/6)^x how would I do this since it is a fraction?
(1 vote)
• think about what happens when you have 2^x. At x=0, you get 1 and as x gets bigger, it increases exponentially (1,2)(2,4)(3,8). On the other side, as x goes negative, it turns to fractions (-1,1/2)(-2,1/4), etc. Fractions would do the opposite such as (1/2)^x. 0 would still give 1, but to the right you get (1,1/2)(2,1/4) etc. and to the left you would get (1/2)^-1 = 2^1, so (-1,2)(-2,4)(-3,8) etc.
Your problem has much more than a fractional base, you have a scale factor of -1 along with the fractional base. The negative reflects it across the x axis, the 2 vertically stretches the function, and the base of 1/6 has it approaching negative infinity as you go to the left and 0 as you go to the right. If x=0, you would be at (0,-2), at -1 it would be -2(6)=-12, at -2 it would be -2(6)2=-72, etc. to the right, at 1, it would be -2*1/6 = -1/3, at 2 it would be -2*1/6^2=-1/18, etc.
• Where did you go to college?
• whats the difference between 3x2^x and 2x3^x? wouldn't you get the same answer?
• It would help to recall the definitions of exponential.
`3*2^x`: the graph starts at `3` (`x=0`), then doubles for every increment of `x`.
`2*3^x`: the graph starts at `2` (`x=0`), then triples for every increment of `x`.
Swapping the numbers therefore results in different exponential functions! Hope this helped.
(1 vote)
• Is it right to say that the exponential and linear functions are geometric and arithmetic sequences respectively?