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# For each of the following functions

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Joined: 22 Aug 2016
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For each of the following functions [#permalink]  23 Dec 2016, 12:37
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For each of the following functions, give the domain and a description of the graph y=f(x) in the xy plane, including its shape, and x and y intercepts?

1) f(x) = -4
2) 100 - 900x
3) f(x) = 5 - (x+20)^2
4) f(x) = $$\sqrt{x+2}$$
5) f(x) = x + I x I

Does anyone know how to solve this question?

Thank you
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: For each of the following functions [#permalink]  23 Dec 2016, 15:14
Expert's post
They key is to understand the meaning of domain. For all values of x for which f(x) is a real number a set of such value is called the domain.

So try and find things like values where the function is imaginary or a point where the value of f(x) suddenly goes to infinity.

Case no 4 i your question is example of imaginary value of f(x).

Example of a function suddenly going to infinity is $$f(x)= \frac{1}{x}$$ Here domain of f(x) is all real number except x=0.

1) f(x) = -4
This is constant function, ie for any value of x you will have a constant value of y so f(x) is defined for all real values of x.

Thus domain of this is the set of all real numbers R.

2) f(x) = 100 - 900x
This is a sum of a constant and a linear function. Both functions are defined for all real numbers

Thus domain of this is the set of all real numbers R.

3) f(x) = 5 - (x+20)^2
This is a sum of a constant and quadratic function. Both functions are defined for all real numbers

Thus domain of this is the set of all real numbers R.

4) f(x) = $$\sqrt{x+2}$$

Here is x < -2 then f(x) is undefined. for any other value f(x) is defined.

Here the domain x all values of $$x \geq -2$$.

5) f(x) = x + |x|

This is a sum of a constant and modulous function. Both functions are defined for all real numbers

Thus domain of this is the set of all real numbers R.
_________________

Sandy
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Re: For each of the following functions   [#permalink] 23 Dec 2016, 15:14
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