describe how you determine the equation of a function of the form y=b^x, where b>0 if you are given its graph.

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Posts: 1269

describe how you determine the equation of a function of the form y=b^x, where b>0 if you are given its graph.

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Posts: 1275

It's just a line with slope b that passes through the origin. If I'm understood what you were asking, that is.

now you got me sittin here playin with my balls tryin to figure out what youre talking about. -swick825

Posts: 9316

y=mx+b? thats slope intercept form. i dont know what this carrot shit is. maybe its similar?

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Posts: 1275

Ah, fuck, I misread the question.

y=b^x is an exponential graph. Without a constant term, it'll pass through the point (0,1) and have a horizontal asymptote at y=0. Also, the slope of the graph at any point is equal to the y-value, so given a graph, you should be able to figure out your b-value from that.

y=b^x is an exponential graph. Without a constant term, it'll pass through the point (0,1) and have a horizontal asymptote at y=0. Also, the slope of the graph at any point is equal to the y-value, so given a graph, you should be able to figure out your b-value from that.

now you got me sittin here playin with my balls tryin to figure out what youre talking about. -swick825

Posts: 5819

if b=1 it is a horizontal line passing through (0,1). Otherwise it has a y intercept at (0,1) and increases exponentially to the right of (0,1) and decreases to the asymptote on the horizontal line 0 to the left of the point. Ill see if I can get a picture for you.

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Posts: 5819

this is if b is a constant term... If be is a variable, its completely different

That made my hand get a brain freeze

Do you need a tissue after that steeze?

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Posts: 2926

carrots=exponents

so y=b[to the]x is the same as y=b^x and the same as y=b[superscript]x

so y=b[to the]x is the same as y=b^x and the same as y=b[superscript]x

Posts: 1275

That's pretty much it.

Essentially, it'll be in the form of y=b^x + c, with c being the y-intercept. Just look at the graph, find the y-intercept for your c-value, and then a couple other points (probably x=1, x=-1, x=2, x=-2, etc..), and use them to find your b-value.

For example, if you have points (0,4), (1,5), (2,13), (3,31) - you can see that your y-intercept, therefore your c-value, is 4. From there, you know it's in the form of y=b^x + 4, and can find the b-value by looking at the other points --> b^1 + 4 = 5 --> b^2 + 4 = 13 --> b^3 + 4 = 31...

From there, you should be able to see that, in this case, b=3, and there you go. y=3^x + 4

I hope that made sense.

Essentially, it'll be in the form of y=b^x + c, with c being the y-intercept. Just look at the graph, find the y-intercept for your c-value, and then a couple other points (probably x=1, x=-1, x=2, x=-2, etc..), and use them to find your b-value.

For example, if you have points (0,4), (1,5), (2,13), (3,31) - you can see that your y-intercept, therefore your c-value, is 4. From there, you know it's in the form of y=b^x + 4, and can find the b-value by looking at the other points --> b^1 + 4 = 5 --> b^2 + 4 = 13 --> b^3 + 4 = 31...

From there, you should be able to see that, in this case, b=3, and there you go. y=3^x + 4

I hope that made sense.

now you got me sittin here playin with my balls tryin to figure out what youre talking about. -swick825

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sorry y=2^x not z even though it would work the same way as a variable

That made my hand get a brain freeze

Do you need a tissue after that steeze?

Do you need a tissue after that steeze?

Posts: 52

He asked how to determine the function, not what the graph looked like, but the graphs are good anyway to help.

If you are determining a function of the form y=b^x, then you are determining the value of b based on the graph. This is very easy. When x=1, y=b. So read the value of the graph at x=1 and that is the value for b.

If you are determining a function of the form y=b^x, then you are determining the value of b based on the graph. This is very easy. When x=1, y=b. So read the value of the graph at x=1 and that is the value for b.

--

digerati1338

digerati1338

Posts: 20319

holy shit

thesurfacelab.blogspot.com

Posts: 1269

Can you explain this any further? I'm really not even sure how that works. I know youve pretty much simplified it, but I dunno what you mean when you say y=b.. like i need to know how to get the transformations, and the rest of the shit

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fuck, i just wrote some help and it didnt work

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Posts: 4595

scan your graph and post it,

transformations are easy. in the form y=ab^x + c. c is the vertical displacement, it can be up or down (ex, if c= -2 shift your graph down 2 units.)

a is whether the graph is reflected in the x axis or stretched/compressed vertically. (if its 1 the graph doesnt change, if its -3 then reflect the graph in the x axis and stretch it by a factor of 3)

b determines whether the graph will be exponential growth, or exponential decay. google it. (its never negative)

if x has a negative sign in front of it then the graph is reflected in the y axis. (ex. -x + 3 will be a (in order) a shift to the left by 3 and THEN a reflection in the y axis.)

so if your equation is y= -3(4)^x-3 +6 shift right 3, reflect in the x, then shift up 6. you find the values of c and whats around x by looking at the graph.

to find a and b use two points on the graph, plug them in the equation y=ab^x + c, you will now have 2 equations (1 and 2 ) in equation 1 solve for a, then plug that into equation 2 to solve for b. put it all together and youll have your finished equation

that probably doesnt make sense

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Posts: 3047

this is a simple math problem holy shit i havent been paying attention the last 2 years of high school

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Posts: 421

what do you mean by transformations? like of the graph? because the transformations are y=t+- b^a(x+-h)

the t moves the graph up and down. the h moves the graph left and right. - numbers move it right and + numbers move it left. and a makes it grow and shrink

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