Graph the exponential function \( g(x)=-\left(\frac{1}{4}\right)^{x}-3 \)

To graph the exponential function \( g(x)=-\left(\frac{1}{4}\right)^{x}-3 \), start by identifying the key features. The base \( \left(\frac{1}{4}\right) \) indicates a decreasing function because it’s less than one. As \( x \) increases, \( g(x) \) approaches -3, which is the horizontal asymptote of the graph. When \( x = 0 \), \( g(0) = -1 - 3 = -4 \); plot that point. As \( x \) approaches negative infinity, the function rises steeply above (-3). Draw a smooth curve that approaches -3 but never touches it, dipping below -3 on its left side. Another cool aspect of this graph is its reflectional property. Because you’re working with a negative function, the graph is reminiscent of a familiar shape. The negative sign in front of the exponential part means that it mirrors the typical exponential curve that would rise steeply into positive territory. Instead, you'll see it gracefully descend from above and tail off just above the horizontal asymptote at -3. So, it’s almost like you’re flipping the standard exponential curve upside down!