the graph of $f(x)=2^{x}$ is given below. write the equation of a function $g(x)$ which would shift the…
the graph of $f(x)=2^{x}$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ right 2 units and down 5 units.
Answer
Explanation:
Step1: Horizontal shift
For a function (y = f(x)), shifting it right (h) units gives (y = f(x - h)). Here (h = 2), so (f(x)) becomes (2^{x - 2}).
Step2: Vertical shift
Shifting a function (y = f(x)) down (k) units gives (y = f(x)-k). Here (k = 5), so (g(x)=2^{x - 2}-5).
Answer:
(g(x)=2^{x - 2}-5)