I need to know what the graph would look like for these equations?

Question

I need to know the graphing details for these

y=2^x
y=log2^x

What would these represent on a graph?

Answer 1

Hi,

y = 2^x is an exponential function with the base of 2 being larger than 1. That means the shape of the graph will be a curved line that crosses the y axis at 1 and bends and shoots up faster and faster on the right hand side through (1,2), (2,4), (3,8), (4,16), etc. The graph crosses the y axis at 1 and continues to get closer and closer to the negative x axis, but it never really gets there. It goes through (-1,½),
(-2,¼), and (-3,1/8), etc.

y = log 2^x

The graph of just y = log x is a curved line that crosses the x axis at 1 and gradually goes up and to the right of that with the y values slowly increasing along a curve going up very gradually. Between 1 and 0, the graph shoots down along the right hand edge of the y axis getting ever and ever closer but never touching or crossing it. There is no log curve for y = log x to the left of the y axis.

In the equation y = log 2^x, x value can now be negative because 2 raised to a negative power still gives a positive fractional number, so the graph will occur both for negative and positive values. The really neat thing about this graph is that when you are taking the log of something raised to a power, you can move the exponent in front of the log times the log of the base. That means log 2^x is the same as x * log 2.

Since log 2 is always the same value x * log 2 is an equation of the form y = mx, where m = log 2. This is a linear equation through the origin with a slope of log 2. This graph goes through the points (-2,-.602), (-1,-.301), (0,0), (1,.301), (2,.602), (3,.903), (4,.1.204).


I hope those help!! :-)

Answer 2

it is going to be falling from left to precise simply by fact it has damaging slope. you will desire to positioned it interior the slope-intercept variety (y=mx+b) to discover the slope (m) and the y-intercept (b). So, x+y=5 y= - x+5 right here, slope is - one million so your line would be falling from left to precise and it will intercept the y axis at 5.

Answer 3

y = 2^x is here:
http://s210.photobucket.com/albums/bb64/oregfiu/?action=view¤t=exponential_curve.jpg
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y=log2^x needs some brackets
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