# Graphing Function: (x^2 + x -12)/(x-4)

• Government$In summary, the conversation discusses finding the roots and sketching the function (x^2 + x -12)/(x-4). The first derivative is found to have roots at 4 - 2√2, 4 + 2√2, and 4, with the max and min at 4 - 2√2 and 4 + 2√2 respectively. However, when plugged into the function, the values are 3.32 and 16.47, leading to the question of how a min can be greater than a max. It is explained that this is possible due to the graph being effectively two unconnected graphs on either side of x = 4, with one having a Government$

## Homework Statement

I should sketch function (x^2 + x -12)/(x-4).

## The Attempt at a Solution

I have problem with first derivative i find it to be (x^2 - 8x +8)/(x-4)^2 with roots at 4 - 2√2, 4 + 2√2, and 4(we lose four because f is not defined at 4). Where at 4 - 2√2 f is at max and at 4 + 2√2 f is at min. But when i plug those two roots in f i find that when x 4 - 2√2 f is = 3.32 and when i plug 4 + 2√2 i find f to be 16.47. How come min is greater then max? Is that even possible?

Government$said: ## Homework Statement I should sketch function (x^2 + x -12)/(x-4). ## The Attempt at a Solution I have problem with first derivative i find it to be (x^2 - 8x +8)/(x-4)^2 with roots at 4 - 2√2, 4 + 2√2, and 4(we lose four because f is not defined at 4). Where at 4 - 2√2 f is at max and at 4 + 2√2 f is at min. But when i plug those two roots in f i find that when x 4 - 2√2 f is = 3.32 and when i plug 4 + 2√2 i find f to be 16.47. How come min is greater then max? Is that even possible? Sure it is possible. They are only a local max and a local min. Start filling in your sketch of the rest of the function. You'll see what's happening. I figured it out by myself when i sketched graph. My professor didn't mention local max and min, he only talked about absolute. Thank you anyway. Hi Government$!
Government\$ said:
… But when i plug those two roots in f i find that when x 4 - 2√2 f is = 3.32 and when i plug 4 + 2√2 i find f to be 16.47. How come min is greater then max? Is that even possible?

At x = 4 it goes off to infinity.

The graph is effectively two unconnected graphs either side of x = 4, one with a maximum and one with a minimum …

since they're unconnected, there's no reason why the maximum should be more than the minimum!

## 1. What is the domain of the given function?

The domain of this function is all real numbers except x = 4, since division by 0 is undefined.

## 2. How do I graph this function?

To graph this function, you can plot points by choosing different values for x and solving for the corresponding y values. You can also use a graphing calculator or software to plot the function.

## 3. What are the intercepts of this function?

The x-intercept of this function is (-3, 0) and the y-intercept is (0, -3).

## 4. What is the end behavior of this function?

As x approaches positive or negative infinity, the function approaches the horizontal asymptote y = 1.

## 5. What is the relationship between the function and its graph?

The graph of this function is a parabola that is shifted 4 units to the right and 3 units down from the standard parabola y = x^2. The function itself represents the ratio between the value of the function and the value of x at any given point on the graph.

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