Understanding the Range of Functions in College Algebra

When tackling College Algebra, a solid understanding of functions and their ranges is crucial—especially if you're gearing up for the CLEP exam. Let’s dig into determining the range of the function ( f(x) = 3x - 2 ). It's simple yet essential for many latent mathematic miracles in your future exams.

So, what is the range of ( f(x) = 3x - 2 )? Is this a trick question? Nope, it’s straightforward. The answer is 'all real numbers.' You see, this linear function can take any real number as an input, which means it can produce any real number as an output. Let’s break that down a bit.

Imagine ( x ) as a buddy who can wear any outfit in the wardrobe of real numbers. Whether he picks a negative number, zero, or a positive integer, he can do it freely, without restrictions. Now, what do those outfits do when it comes to the output? If we plug various values into our function, like ( x = 0, 1, ) or even something wild like ( -100 ), we’ll find that ( f(x) ) adjusts accordingly.

Here’s the thing: when you substitute any real number into ( 3x - 2 ), it’s like you’re adjusting the thermostat. Regardless of how high or low you set the temperature (or input), the result is an output that stretches infinitely across the number line. Thus, the range of ( f(x) = 3x - 2 ) really is all real numbers, making option A the only correct choice in this scenario.

Now, just for a moment, let’s play around with what that really means. Options B, C, and D—those state options that only limit outputs to non-negative, positive, or negative numbers—are like a straitjacket for our function. They don't allow it the freedom to explore all possibilities. It’s important to hold onto this idea: a function's range can be expressive, reflective of its inputs. It shouldn’t be put in a box when it has the potential to extend far and wide.

Why does it matter for your CLEP prep, you ask? Well, understanding function ranges can help you with more complex topics like inequalities, sequences, and even calculus fundamentals later down the road. It’s all interconnected, like a giant web of mathematical relationships.

Understanding linear functions serves as a foothold for much of algebra, and once you grasp that ( f(x) = 3x - 2 ) envelops all real numbers, you’re on a pathway to success. In math, as in life, the more possibilities you embrace, the more robust your understanding becomes.

So next time you see a function, don’t just plug in numbers without thought. Consider what outputs it can yield, reflect on its range, and you’ll find your confidence growing right alongside your mathematical savvy. Happy studying, future algebra whiz!