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.\n( h(x)=3^{x - 2}+2 )\nfunction ( h(x)=3^{x - 2}+2 )? choose the correct answer below.\na. the graph of ( f(x)=3^{x} ) should be horizontally shifted 2 units to the left and vertically shifted 2 units downward.\nb. the graph of ( f(x)=3^{x} ) should be horizontally shifted 2 units to the right and vertically shifted 2 units upward.\nc. the graph of ( f(x)=3^{x} ) should be horizontally shifted 2 units to the right and vertically shifted 2 units downward.\nd. the graph of ( f(x)=3^{x} ) should be horizontally shifted 2 units to the left and vertically shifted 2 units upward.\ngraph ( h(x)=3^{x - 2}+2 ) and its asymptote. graph the asymptote as a dashed line. use the graphing tool to graph the function.\nfind the equation of the asymptote for ( h(x)=3^{x - 2}+2 ) using the graph.\n( y = 2 )\n(type an equation.)\nobserve the graph and find the domain of ( h(x)=3^{x - 2}+2 ).\n(type your answer in interval notation.)

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.\n( h(x)=3^{x - 2}+2 )\nfunction ( h(x)=3^{x - 2}+2 )? choose the correct answer below.\na. the graph of ( f(x)=3^{x} ) should be horizontally shifted 2 units to the left and vertically shifted 2 units downward.\nb. the graph of ( f(x)=3^{x} ) should be horizontally shifted 2 units to the right and vertically shifted 2 units upward.\nc. the graph of ( f(x)=3^{x} ) should be horizontally shifted 2 units to the right and vertically shifted 2 units downward.\nd. the graph of ( f(x)=3^{x} ) should be horizontally shifted 2 units to the left and vertically shifted 2 units upward.\ngraph ( h(x)=3^{x - 2}+2 ) and its asymptote. graph the asymptote as a dashed line. use the graphing tool to graph the function.\nfind the equation of the asymptote for ( h(x)=3^{x - 2}+2 ) using the graph.\n( y = 2 )\n(type an equation.)\nobserve the graph and find the domain of ( h(x)=3^{x - 2}+2 ).\n(type your answer in interval notation.)

Answer

Explanation:

Step1: Determine the domain of an exponential function

For any exponential function of the form (y = a^{x - h}+k) (where (a>0,a\neq1)), the domain is all real numbers. The function (h(x)=3^{x - 2}+2) is an exponential function. There is no restriction on the value of (x) for which the function (h(x)) is defined.

Step2: Write the domain in interval notation

The set of all real numbers in interval notation is ((-\infty,\infty))

Answer:

((-\infty,\infty))