Expert: Paul Klarreich - 2/3/2012

Question
Consider the following equation: f(x) = -4√x + 1. (-4 times square root of x, plus 1)
1. What are the domain and range of this function?
2. What are the x-intercept(s).

Answer
Questioner:Hiral
Country:New Jersey, United States
Category:Calculus
Private:Yes  <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<  changed
Subject:Calculus

Question:

Consider the following equation: f(x) = -4√x + 1. (-4 times square root of x, plus 1)
1. What are the domain and range of this function?
2. What are the x-intercept(s).

1. Domain:  
When you have a function specified algebraically, the domain is always:

D = { all real numbers that don't cause trouble }

Trouble? Could be:

A-bad. a square root of a negative number.

B-bad. a fraction with 0 in the denominator.

So you need  x >= 0, or you get an A-bad.

You don't have any fractions, so never mind B.

Range:

Look at the possible values of:

A.  √x   ---  must be >= 0

B. -4√x   ---  must be ....?

C.  -4√x + 1 --- must be ....?


2. x-intercepts:  Solve y = 0 for x