question 26\nstarting with the graph of ( f(x)=6^{x} ), write the equation of the graph that results…

question 26\nstarting with the graph of ( f(x)=6^{x} ), write the equation of the graph that results when:\n(a) ( f(x) ) is shifted 6 units upward. ( y= )\n(b) ( f(x) ) is shifted 2 units to the left. ( y= )\n(c) ( f(x) ) is reflected about the ( x )-axis. ( y= )\nquestion help: video

question 26\nstarting with the graph of ( f(x)=6^{x} ), write the equation of the graph that results when:\n(a) ( f(x) ) is shifted 6 units upward. ( y= )\n(b) ( f(x) ) is shifted 2 units to the left. ( y= )\n(c) ( f(x) ) is reflected about the ( x )-axis. ( y= )\nquestion help: video

Answer

Explanation:

Step1: Vertical shift formula

For a function (y = f(x)), shifting (k) units upward gives (y=f(x)+k). Here (f(x)=6^{x}) and (k = 6), so (y=6^{x}+6).

Step2: Horizontal shift formula

For a function (y = f(x)), shifting (h) units to the left gives (y = f(x + h)). Here (f(x)=6^{x}) and (h=2), so (y=6^{x + 2}).

Step3: Reflection about the x - axis formula

For a function (y = f(x)), reflection about the (x) - axis gives (y=-f(x)). Here (f(x)=6^{x}), so (y=-6^{x}).

Answer:

(a) (y = 6^{x}+6) (b) (y = 6^{x + 2}) (c) (y=-6^{x})