# Thread: graphing functions

1. ## graphing functions

For this question I am supposed to graph the function and determine the interval(s) (if any) on the real axis for which f(x) is greater than or equal to 0. My question is this: f(x) = x^2 - 4x
Can you help me with it?

Thank you for your time,
starrynight

2. See where the graph is above the x-axis.

3. Originally Posted by red_dog
See where the graph is above the x-axis.
I get the graph but how do I find the intervals?

4. Hello starrynight
Originally Posted by starrynight
I get the graph but how do I find the intervals?
Look at where the graph of $\displaystyle f(x)$ crosses the $\displaystyle x$-axis: $\displaystyle x = 0$ and $\displaystyle x = 4$. These two points divide the $\displaystyle x$-axis into 3 intervals:

• $\displaystyle x \le 0$

• $\displaystyle 0 \le x \le 4$

• $\displaystyle 4 \le x$

The question asks you for the interval(s) for which $\displaystyle f(x) \ge 0$. In other words, in which of the three intervals above is the graph of $\displaystyle f(x)$ on or above the $\displaystyle x$-axis.

So, which one(s) is it?

5. I think the answer is $\displaystyle 0 \le x \le 4$

6. No, this is the interval where the graph goes below the x-axis; in other words, where $\displaystyle f(x) \le 0$.

So you want the two intervals $\displaystyle x \le 0$ and $\displaystyle 4 \le x$.

7. Originally Posted by starrynight
For this question I am supposed to graph the function and determine the interval(s) (if any) on the real axis for which f(x) is greater than or equal to 0. My question is this: f(x) = x^2 - 4x
Can you help me with it?

Thank you for your time,
starrynight
Following up on red_dog's graph, for each $\displaystyle x$ you need to get a positive or null image, can you see what are those intervals then?

8. ## graphing/writing functions

I am having trouble with problem 74. I don't really know how to approach the problem. The directions say to write the height , h , as a function of x.

I would highly appreciate it if someone could help me out.
--Thanks

9. h = 2 - x^(1/3) ?

10. As far as I can see, $\displaystyle h$ is the vertical distance
between the y-coodinate and a horizontal asymptote of 2.

So simply, $\displaystyle h= |2-\sqrt[3]{x}|$

Strictly speaking, I don't think the absolute value is needed.

11. So following up on songoku and Deco, is the correct form of writing the function with the square root or should i leave it as x^1/3?

--Thanks again.

12. It's a cube root, and they both represent the exact same thing.