## What is the Range of the Function f(x) = 3×2 + 6x – 8?

Wow, the situation you described sounds quite intense. It seems like there was an event involving your sister that caused you to make the difficult decision to ghost your family and fiance. Ghosting, which involves abruptly cutting off all communication with someone, can be a challenging action to take, especially when it involves loved ones.

While I don’t have all the details about what exactly happened, it’s clear that whatever your sister did must have been significant enough for you to feel the need to distance yourself from everyone close to you. Ghosting is often seen as a way of protecting oneself or taking a break from certain relationships.

However, it’s important to consider whether ghosting is truly the best approach in this situation. Communication is vital for resolving conflicts and addressing issues within relationships. Taking some time apart may provide an opportunity for reflection and healing, but ultimately finding healthy ways to address and work through these challenges might be more beneficial in the long run.

Remember that every situation is unique, and only you can determine what actions are best for your own well-being. Seeking support from trusted friends or professionals who can offer guidance during this difficult time might also be helpful.

## Determining the Range of the Function

When it comes to understanding the range of a function, we need to analyze how the function behaves and what values it can take on. In this case, we’ll be focusing on the function f(x) = 3x^2 + 6x – 8. Let’s dive in and explore!

To determine the range of this function, we first need to consider its behavior as x varies. One way to approach this is by examining the graph of the function. By plotting various points on a coordinate plane, we can get a visual representation of how f(x) behaves.

Another approach involves analyzing the nature of quadratic functions. Since our given function is in the form of a quadratic equation (ax^2 + bx + c), with “a” being non-zero, we know that it represents a parabola opening upwards or downwards.

In this specific case, since “a” is positive (3), our parabola opens upwards. This means that there exists a minimum point on the graph where all values above it are greater than or equal to that minimum value.

To find out more about this minimum point and thus determine our range accurately, we can use calculus techniques such as finding critical points and evaluating them for extrema. However, for simplicity’s sake, let’s stick to basic algebraic reasoning here.

Since our parabola opens upwards and has no maximum point (as there is no upper limit for x), its range will extend from its minimum point indefinitely towards positive infinity. Thus, we can conclude that f(x) has a range from its minimum value up to positive infinity.

In summary, based on our analysis of both graphical and algebraic aspects, we determined that the range of f(x) = 3x^2 + 6x – 8 extends from its minimum value upwards without any upper bound.