Question

The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n +c.what does the graph tell you about the value of a in this function?

Answer 1

Answer:

a is less than 0

Step-by-step explanation:

Answer 2

The value of a in this function is a is less than 0 .

What is  radical function?

A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions. An example of a radical function would be. y=√x.

According to the question

Radical function that can be written in the form

$f(x)=a(x+k)^{1/n} +c.$ ------------------------(1)

By solving this equation we will get value of a and c

differentiating the equation

$f'(x)=\frac{1}{n}* (a(x+k)^{1/n-1})$

therefore

$((x+k)^{1/n-1}) > 0$

As graph is decreasing monotonically  

$\frac{a}{n} < 0$

as n will be always n>0 ,

so a < 0

Now taking value of f(x)= 0 in equation (1)

$f(x)=a(x+k)^{1/n} +c$

$0 =-a(x_{0} + k)^{1/n} +c$   as (a < 0)

$0=-a(k)^{1/n} +c$

$-c =-a(k)^{1/n}$  multiplying (-1) both side

$c =a(k)^{1/n}$  

i.e

c > 0

Hence, the value of a in this function is a is less than 0 .

To know more about Radical function here:

https://brainly.com/question/27847549

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