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

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

# Graphs of exponential functions (old example)

Sal matches the following four functions to their appropriate graphs: y=2^x, y=-3^x, y=2-(1/3)^x, y=(1/2)^x-2. Created by Sal Khan.

## Want to join the conversation?

• Why -3^x when x=0 results to -1
• if it were written as (-3)^x, when x=0, then y would equal 1, but it is written as -3^x without parenthesis, therefore when x=0, y=-1
• Why does x⁰ = 1?
• Anything to the 0 power is 1. Lets look at a simple example, not some variable.

Follow this pattern `3^1 = 3`, `3^2 = 9`, `3^3 = 27` By observing this pattern we can see that by increasing you are multiplying by 3, and when you decrease you're dividing by 3. `3^1 = 3 / 3 = 1` So now we know that `3^0 = 1`.

Let's look at another example to prove that anything to the 0 power is 1.

Here's one basic law of exponents.
`n^x / n^y = n^(x - y)`. Example `3^5 / 3^2 = 3^3`, according to the law.
`3^3 / 3^3 = 3^(3 -`` 3)` or `3^0`. When we look at this problem, we can tell anything divided by itself is 1 . `So 3^0` is also proven to be `1`.

Hopefully I Haven't Confused You.
• Also, how can I tell if an asymptote is horizontal or vertical in a logarithm
• An asymptote in an exponential function is always horizontal (growth or decay do not differentiate), while in a logarithm is it vertical (because it is the inversion of an exponential function).
(1 vote)
• what is the deductive reasoning in 4th graph?
(1 vote)
• Deductive reasoning takes existing facts and uses them to draw another conclusion. Here the initial facts are:
`1`: which 3 graphs we've already used
`2`: the remaining graph and remaining function that must be used
Therefore the remaining graph goes with the remaining function.

See https://www.khanacademy.org/math/precalculus/seq_induction/deductive-and-inductive-reasoning for a discussion of what deductive reasoning is.
• in the whole video, which line is x and y??
(1 vote)
• In a coordinate system, the x-axis is the horizontal line and the y-axis is the vertical line.
• Is there a specific formula for this? I'm still confused how to solve these?
• Maybe it would help to redo some of the earlier videos and rework the problems there. Sometimes the second time through clears up a lot of confusion.
(1 vote)
• What is the graph (4^x)-4
• How would I solve some thing like...
f(x) = -2(1.5)[to the power of x] , g(x) = -2(1.5)[to the power of x] - 2?

What I mean is how do I go through the process for any question like that.

Or is there a video where I could find something like this?
• At , what would the graph be if the equation were the other way: `y = (-3)^x`?