Question

Find the domain and range of each function.

f(x) = -sqrt{x}

h(x) = sqrt{x + 1}

Answer 1

Let P = (x, y) be a point on the graph of y = x^2 - 8.

A. Express the distance d from P to the point (0, -1) as a function of x.

B. What is d if x = 0?

C. What is d if x = -1?

Answer 2

you know that sqrt(n) is defined only for n >= 0
So, sqrt(x+1) is defined only for x+1 >= 0
Sketch the graph and you can easily determine the range.

For P(x), just use the usual distance formula
sqrt((x-0)^2 + (y+1)^2) = sqrt(x^2 + (x^2-8+1)^2)
Now just plug in your values.