which steps will translate $f(x)=3^{x}$ to $g(x)=3^{x + 1}+4$?\nshift $f(x)=3^{x}$ one unit up and four…

which steps will translate $f(x)=3^{x}$ to $g(x)=3^{x + 1}+4$?\nshift $f(x)=3^{x}$ one unit up and four units to the right.\nshift $f(x)=3^{x}$ one unit up and four units to the left.\nshift $f(x)=3^{x}$ one unit to the right and four units up.\nshift $f(x)=3^{x}$ one unit to the left and four units up.

which steps will translate $f(x)=3^{x}$ to $g(x)=3^{x + 1}+4$?\nshift $f(x)=3^{x}$ one unit up and four units to the right.\nshift $f(x)=3^{x}$ one unit up and four units to the left.\nshift $f(x)=3^{x}$ one unit to the right and four units up.\nshift $f(x)=3^{x}$ one unit to the left and four units up.

Answer

Explanation:

Step1: Recall function - translation rules

For an exponential function (y = a^{x}), if we have (y=a^{x + h}+k), a horizontal shift of (h) units and a vertical shift of (k) units occur. If (h>0), the graph shifts (h) units to the left; if (h < 0), the graph shifts (|h|) units to the right. If (k>0), the graph shifts (k) units up; if (k < 0), the graph shifts (|k|) units down. We are given (f(x)=3^{x}) and (g(x)=3^{x + 1}+4).

Step2: Analyze the horizontal - shift

Comparing (f(x)=3^{x}) and (g(x)=3^{x + 1}+4), for the exponent part, we have (x) in (f(x)) and (x + 1) in (g(x)). Using the rule (y=a^{x+h}), where (h = 1), the graph of (y = 3^{x}) shifts 1 unit to the left.

Step3: Analyze the vertical - shift

In (g(x)=3^{x + 1}+4), the constant term is (4). Using the rule (y=a^{x+h}+k) with (k = 4), the graph of (y = 3^{x+1}) shifts 4 units up.

Answer:

Shift (f(x)=3^{x}) one unit to the left and four units up.