Evaluating and Graphing Exponential Functions

We know about functions where exponents are raised to different variables, to produce quadratics, cubics, quartics, and so forth. But what about when the variable itself is an exponent? This is called an exponential function, and they are important for modeling things like population growth and other real-world scenarios. Let's learn about them!

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[Tusharplays]

I'm in 7th grade rn from Bangladesh and i have none of this in my syllabus (they're just teaching basic multiplication and division of polynomials, and i've not even been introduced to pythagorean theorem in school yet.), yet i've completed almost a half of this series. And soon i'll get to learn trigonometry from your series, which is nowadays here taught in 9-10th grade. Thanks a lot to you professor because of you my parents aren't regretting paying wifi bills. ❤

[cheressacargill]

This video was the most helpful thing I have seen in a long time! I have a quiz on this stuff today and totally did not understand when to reflect across x / y axis and this video was so helpful, thank you!!

[jamesferris]

You are a magical legend of a man who flattens the flat Earthers and helps me with my Algebra homework. Thank you, Professor Dave.

[DenovoTutor]

Your videos are amazing! You inspired me to start my own Tutoring channel :)

[joelortiz]

I like doing exponential functions, but sometimes I struggle a little, sometimes I get it right. What I get It More right is the Chart with Numbers with power, like for instance, 3 to the -3rd Power, and I can figure it out as I understand.

[masongarofalo]

Professor Dave explains is the best intro on yt

[ahmedmazher]

Y = -2 ^ x
If x is even y is positive
If y is odd y is negative
How to graph it or i misunderstood some thing

[RadoHudran]

What I didn't get at first was him saying at 1:25 Base a must be positive.
Then later he says at 4:30 that you can put a negative sign there for reflection acroos x-axis.

I think i just means that (-3)^x is not an exponential function while -3^x is

[lvrhees]

Thank you so much omg your the only one who explains it where I understand

[amishaparmar]

How can the graph of a>1 and b<0 dip down to the right?? It should dip down to the left, shouldn't it?? Or have i misunderstood something??

[key]

how do you know what the horizontal asymtipbe is

[santhoshmouli]

Hi Dave
I have small doubt
In the middle of your explanation
You say that a(base)<1 and b(exponent)>0 the function will Dip down to the right, i understand this as per exponential function y=(1/2)to the x
But you also say a(base)>1 and b(exponent)<1 the function will Dip down to the right, i think this second one was not correct as per exponential function y=2 to x power, were base is >1 and exponent is <0 the function dip left side of the grap not right side
That's my doubt is it correct or i get confused

[priencessme]

Idk anything abt em 😂😂 I draw this graphs easily by different method however thanks sur because of you I got full marks in exam told u abt it yesterday ryt? Ur my own teacher 😂😂 where r u from, ur so talented ..my frnds said that you've studied tht much that u can get mad easily so sorry if u feel bad really how old r u ? How much years does it takes you to reach here hope you'll reply me by honesty

[Ramonoemoganedi]

When we now move away from x=0 to the largest negative values of x like x -1or x -2 provided y=3/4 or y = 1/2 how to plot the graph.

[OkSid]

I've got to go on note here! The rational functions were my least favorite! They are as ugly as the fractions that produce them!