Function \( f \) is defined by \( f(x)=5^{x} \) Select the range of the function. \( y>0 \) \( y>5 \) \( y \geq 0 \) \( y \geq 5 \)

The function \( f(x) = 5^x \) is an exponential function where the base \( 5 \) is greater than \( 1 \). This means that as \( x \) approaches negative infinity, \( f(x) \) approaches \( 0 \) but never actually reaches it. Conversely, as \( x \) approaches positive infinity, the values of \( f(x) \) grow without bound. Therefore, the range of \( f(x) \) is all positive real numbers, which can be expressed as \( y > 0 \). While many might think that exponential functions only apply in mathematical contexts, they have real-world applications too! For instance, they model populations in biology, compound interest in finance, and radioactive decay in physics. Understanding the range allows us to predict outcomes in these areas, ensuring we don't miss the mark when applying calculations in practical scenarios.