## College Algebra (11th Edition)

The parent function is $f(x)=2^x$ (with red) the given function is $g(x)=-2^{x-3}$ (with blue). For every corresponding x-value the following equation is true: $-f(x-3)=g(x)$ This means that the graph is translated 3 units right. Every x-value will be increased by 3. (Because the original f(x) will be equal to f(x-3). For example if x=0 in the original f(0), this will be translated as f(3-3), where x=3. We can see that here, x has increased by 3.) After that it is also reflected across the x-axis. (Because of the -1 coefficient before f(x-3))