If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### 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.
• 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
• 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.
• 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?
• Is it right to say that the exponential and linear functions are geometric and arithmetic sequences respectively?
• You can say that, however technically speaking, the term numbers of sequences (inputs) have to have positive, integer, values (some people use zeroth terms so the term number can be non-zero values). An exponential and linear function can have negative, decimal inputs, so in rigorous mathematical language, you can't say that, but informally speaking, the concepts is very, very similar.
• question why does anything to the power of 0=1?
(1 vote)
• The word exponential growth and linear growth are frequently used in the media. People toss these words around wrongly. With a very easy to follow numerical example ,what exactly does it mean to grow exponentially?
(1 vote)
• In a mathematical sense I believe that to "grow exponentially" simply means that you are modeling growth (such as a population) with an exponential function (usually of the form y=a^x). The reason we use the term exponential growth as opposed to linear growth in media is because we are comparing a growth rate to the behavior of an exponential function. So for example something with a linear growth rate will grow at a steady pace while something that has an exponential growth rate is increasing extremely rapidly after only a small amount of time. We can picture this behavior using the graph of an exponential function, say y=2^x, for every increase in x, y grows faster and faster (when x=1, y=2, when x=2, y=4, when x=4, y=16 etc.) instead of at a constant rate.
Hope this helps! :)