Exponential functions, Algebra

Assignment Help:

Definition of an exponential function

If b is any number like that b = 0 and b ≠ 1 then an exponential function is function in the form,

                                                     f( x ) = b x

Where b is the base and x is any real number.

Notice that now the x is in the exponent & the base is a fixed number.  It is exactly the opposite through what we've illustrated to this point. To this point the base has been the variable, x in most of the cases, and the exponent was a fixed number.  Though, in spite of these differences these functions evaluate in precisely the similar way as those that we are utilized to. 

Before we get too far into this section we have to address the limitation on b. We ignore one and zero since in this case the function would be,

                             f( x ) = 0x  = 0        and f( x) = 1x  = 1

and these are constant functions & won't have several same properties that general exponential functions have.

Next, we ignore negative numbers so that we don't get any complex values out of the function evaluation.  For example if we allowed b = -4 the function would be,

                                   f(x)=(-4)x            ⇒ f (1/2)=(-4)(1/2)=√(-4)    

and as you can illustrates there are some function evaluations which will give complex numbers. We only desire real numbers to arise from function evaluation & so to ensure of this we need that b not be a negative number.

Now, let's take some graphs.  We will be capable to get most of the properties of exponential functions from these graphs.


Related Discussions:- Exponential functions

Arithmatic progression, find the sum upto n terms of the following sequence...

find the sum upto n terms of the following sequence 3+33+333+... n terms

Math, Linda has a total of 225 on 3 tests. The sum of the scores on the fir...

Linda has a total of 225 on 3 tests. The sum of the scores on the first and second tests exceeds her third score by 61. Her first test exceeds her second by 6 points. Find Linda''s

Math, i need help with my math homework

i need help with my math homework

Completing the square process, As a last topic in this section we have to b...

As a last topic in this section we have to briefly talk about how to take a parabola in the general form & convert it into the following form

Functions, f(x)-4x+4 find f(x+h)-f(x)/h

f(x)-4x+4 find f(x+h)-f(x)/h

Rational expressions, I am looking the domain of g^2-6g-55/g. The denominat...

I am looking the domain of g^2-6g-55/g. The denominator here can be also be written as 1g, right?

Equations, if a-b equals 73 what is a

if a-b equals 73 what is a

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd