What is the Range of the Function f(x) = 3×2 + 6x – 8?
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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.
Jessica has a flair for writing engaging blogs and articles. She enjoys reading and learning new things which enables her to write different topics and fields with ease. She also strives to break down complex concepts and make them easy for anybody to comprehend.