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## Algebra (all content)

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

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

# Exponential function graph

We can graph an exponential function, like y=5ˣ, by picking a few inputs (x-values) and finding their corresponding outputs (y-values). We'll see that an exponential function has a horizontal asymptote in one direction and rapidly changes in the other direction. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Can anyone explain to me why a negative power is always a fraction?
• Technically, an exponent expresses multiplication, and is shown with a positive number. The opposite of a positive number is (obviously) a negative number, so in keeping with the rules of exponents, this must somehow be the "opposite" of multiplication, which happens to be division. Therefore, a negative exponent is always a division (written as a fraction).
That's the reason.
• why does any number to the 0 power always become a 1? why not 0?
• As the saying goes, "Do the Math!"
At this stage you may not know all you need to with regard to the properties of exponents.
Here is one explanation that requires knowing that (x^a)/(x^b)= x^(a-b)
You know that, for example, 5/5=1, correct? It is because the numerator and denominator are equal.
Suppose you had (5^6)/(5^6). Since the numerator and denominator are equal, this is also equal to 1.
Now, using the exponential property that (x^a)/(x^b)= x^(a-b), we have
(5^6)/(5^6) = 5^(6-6) = 5^0.
And since (5^6)/(5^6) = 1 and (5^6)/(5^6) = 5^(6-6) that means 5^0 = 1 as well.

You will know lots more about exponential function when you finish this course!
• whats a slope?
• these answer above are all right.but there's another idea about slope.slope of a line can be expressed as a trigonometric function.it's the tangent of the angle formed between the x-axis and the line itself.
• Why Sal drew curved lines between the points. Why not straight lines?
• how do you do negative exponents?
• The first step is to flip them for example
5^-2 would flip the -2 and because all numbers are technically fractions (5=5/ 12=12/1 this applies to any number) you would just flip it so instead of having -2 (or -2/1) you would have 1/2. so when rewritten it would be 5^1/2 then you can plug into your cauclour
(1 vote)
• So no matter what, the graph can't go below the "X-Axis"?
• If a is a positive number, then a^x is greater than 0 for all x. So, the graph of a^x will never intersect, nor go below the x-axis.
• What is the difference between exponents and indices?
• T Ross,

Exponents are notations that indicate a base number is raised to a power or multiplied by itself a given number of times. In writing or word processing programs that allow it, exponents are written as superscript(above the base number). In a plain text editor (like this one), exponents are noted using the *^* symbol.

For example,

2^3 means 2 multiplied together 3 times: 2*2*2 = 8
x^3 means x multiplied together 4 times: x*x*x*x

Indices are a notation that indicates the position of an element in a sequence, array, or matrix. In a word processing program that allows it, indices are shown in subscript (below the name or variable assigned to the sequence). In a plain text editor, indices are indicated using the _. In the example in the video, Sal uses the sequence of numbers -2, -1, 0, 1, 2 for the x values. If you were to call this sequence X, then

X_1 = -2
X_2 = -1
X_3 = 0
X_4 = 1
X_4 = 2
• Don't Positive Exponential Functions always rise upward from the x-axis while the Negative Exponential Function slides downward to the the x-axis. In the Positive function, both x and y values increase I presume, and in the negative the x value increases, while the y value decreases?
• sorry this question stupid but i really suck at math so where does the two in the equation come from?
• Vmone,

If you are talking about the 2 in the column labeled x, that is a value that Sal selected. He selected all of the x values and used them to calculate the y values.