begin by graphing ( f(x)=3^{x} ). then use transformations of this graph to graph the given function. be…

begin by graphing ( f(x)=3^{x} ). then use transformations of this graph to graph the given function. be sure to graph and give the equation of the asymptote. use the graph to determine the functions domain and range. if applicable, use a graphing utility to confirm your hand - drawn graphs.( g(x)=3^{x - 6} )which transformation is needed to graph the function ( g(x)=3^{x - 6} )? choose the correct answer below.( \bigcirc ) a. the graph of ( f(x)=3^{x} ) should be shifted 6 units downward.( \bigcirc ) b. the graph of ( f(x)=3^{x} ) should be shifted 6 units to the right.( \bigcirc ) c. the graph of ( f(x)=3^{x} ) should be shifted 6 units to the left.( \bigcirc ) d. the graph of ( f(x)=3^{x} ) should be shifted 6 units upward.

begin by graphing ( f(x)=3^{x} ). then use transformations of this graph to graph the given function. be sure to graph and give the equation of the asymptote. use the graph to determine the functions domain and range. if applicable, use a graphing utility to confirm your hand - drawn graphs.( g(x)=3^{x - 6} )which transformation is needed to graph the function ( g(x)=3^{x - 6} )? choose the correct answer below.( \bigcirc ) a. the graph of ( f(x)=3^{x} ) should be shifted 6 units downward.( \bigcirc ) b. the graph of ( f(x)=3^{x} ) should be shifted 6 units to the right.( \bigcirc ) c. the graph of ( f(x)=3^{x} ) should be shifted 6 units to the left.( \bigcirc ) d. the graph of ( f(x)=3^{x} ) should be shifted 6 units upward.

Answer

Explanation:

Step1: Recall transformation rules

For a function (y = f(x - h)), the graph of (y = f(x)) is shifted (h) units to the right. For (y=f(x + h)), the graph of (y = f(x)) is shifted (h) units to the left. For (y=f(x)+k), the graph of (y = f(x)) is shifted (k) units upward. For (y = f(x)-k), the graph of (y = f(x)) is shifted (k) units downward.

Given (f(x)=3^{x}) and (g(x)=3^{x - 6}), we can rewrite (g(x)) in the form (y = f(x - h)) where (h = 6) and (f(x)=3^{x}).

Answer:

B. The graph of (f(x)=3^{x}) should be shifted 6 units to the right.