Graphs of Exponential Functions · Exercise 11

The graph of $f\left(x\right)=-\frac{1}{2}{\left(\frac{1}{4}\right)}^{x-2}+4$ is shifted downward $4$ units, and then shifted left $2$ units, stretched vertically by a factor of $4,$ and reflected about the x-axis. What is the equation of the new function, $g\left(x\right)?$ State its y-intercept, domain, and range.

OpenStax, Algebra and Trigonometry 2e · §6.2 Graphs of Exponential Functions · Exercise 11