use transformations of the graph of ( f(x)=e^{x} ) to graph the given function. be sure to give the equation…

use transformations of the graph of ( f(x)=e^{x} ) to graph the given function. be sure to give the equation of the asymptote. use the graphs to determine each functions domain and range. if applicable, use a graphing utility to confirm the hand - drawn graphs.( h(x)=e^{x + 2}-3 )which transformations are needed to graph the function ( h(x)=e^{x + 2}-3 )? choose the correct answer below.( \bigcirc )a. the graph of ( f(x)=e^{x} ) should be shifted to the right by 2 units and shift ( f(x) ) upward by 3 units.( \bigcirc )b. the graph of ( f(x)=e^{x} ) should be shifted to the left by 2 units and shift ( f(x) ) upward by 3 units.( \bigcirc )c. the graph of ( f(x)=e^{x} ) should be shifted to the left by 2 units and shift ( f(x) ) downward by 3 units.( \bigcirc )d. the graph of ( f(x)=e^{x} ) should be shifted to the right by 2 units and shift ( f(x) ) downward by 3 units.

use transformations of the graph of ( f(x)=e^{x} ) to graph the given function. be sure to give the equation of the asymptote. use the graphs to determine each functions domain and range. if applicable, use a graphing utility to confirm the hand - drawn graphs.( h(x)=e^{x + 2}-3 )which transformations are needed to graph the function ( h(x)=e^{x + 2}-3 )? choose the correct answer below.( \bigcirc )a. the graph of ( f(x)=e^{x} ) should be shifted to the right by 2 units and shift ( f(x) ) upward by 3 units.( \bigcirc )b. the graph of ( f(x)=e^{x} ) should be shifted to the left by 2 units and shift ( f(x) ) upward by 3 units.( \bigcirc )c. the graph of ( f(x)=e^{x} ) should be shifted to the left by 2 units and shift ( f(x) ) downward by 3 units.( \bigcirc )d. the graph of ( f(x)=e^{x} ) should be shifted to the right by 2 units and shift ( f(x) ) downward by 3 units.

Answer

Explanation:

Step1: Recall the transformation rules for horizontal shift

For a function (y = f(x + k)), if (k>0), the graph of (y = f(x)) is shifted to the left by (k) units. For the function (h(x)=e^{x + 2}-3), compared to (f(x)=e^{x}), we have (x\to x + 2). So, the graph of (y = e^{x}) is shifted to the left by (2) units.

Step2: Recall the transformation rules for vertical shift

For a function (y=f(x)-k) ((k > 0)), the graph of (y = f(x)) is shifted downward by (k) units. For the function (h(x)=e^{x + 2}-3), compared to (y = e^{x+2}), we have (y=e^{x + 2}-3). So, the graph of (y = e^{x+2}) is shifted downward by (3) units.

Answer:

C. The graph of (f(x)=e^{x}) should be shifted to the left by 2 units and shift (f(x)) downward by 3 units.