Intercepts, domain and range?

• Apr 17th 2008, 12:28 PM
romanianxromo
Intercepts, domain and range?
Let f(x) = {√x, 0 ≤ x ≤ 1
{ 1/x, x > 1

(a). Identify any intercepts
(b). Graph the function
(c). Find the domain and range

I'll be able to graph it, I just can't do a or c
• Apr 17th 2008, 02:07 PM
colby2152
Quote:

Originally Posted by romanianxromo
Let f(x) = {√x, 0 ≤ x ≤ 1
{ 1/x, x > 1

(a). Identify any intercepts
(b). Graph the function
(c). Find the domain and range

I'll be able to graph it, I just can't do a or c

Intercepts imply intercepting with the x-axis or y-axis.

The function would intercept the y-axis at x = 0 which is for the first piece.

$\sqrt{0} = 0$

It's y-intercept is at x = 0.

It's x-intercept is whenever y = 0. Notice that the x-intercept is the same as the y-intercept.

The domain is all real numbers that can go into the function. The square root cannot take any negative values and the $\frac{1}{x}$ cannot take zero, but it's not even a valid piece of the function in that region, so the domain is simply all non-negative reals. The range is just the same.
• Apr 17th 2008, 02:28 PM
romanianxromo
Oh, ok. I see.

So then how would I plug that into my TI 84 + to get the graph?

Y1=(X and 0≤x≤1
Y2=(1/x and x > 1

I got a horizontal line at the point (0,1) is that right?