The function h(x) is a translation of the exponential function,
[tex]g(x) = 2(3)^{x-4}[/tex] is [tex]h(x) = 4(3)^{x-7} - 9\\\\[/tex].
Given that,
The function h(x) is a translation of the exponential function,
[tex]g(x) = 2(3)^{x-4}[/tex]
We have to determine,
What's h(x) if the translation is a vertical stretch by a factor of 2, a vertical shift upward 9 units, and a horizontal shift to the right 7 units?
According to the question,
Exponential function; [tex]g(x) = 2(3)^{x-4}[/tex]
To find the translation in h(x) following all the steps given below.
- Step1; The function h(x) is vertically stretched by 2.
[tex]h(x) = 2(2(3)^{x-4} )\\\\h(x) = 4(3)^{x-4}[/tex]
- Step2; Vertically shift upward by 9,
[tex]h(x) = 4(3)^{x-4} \\\\h(x) = 4(3)^{x-4} - 9[/tex]
- Step3; And a horizontal shift to the right 7 units,
[tex]h(x) = 4(3)^{x-7} - 9\\\\[/tex]
Hence, The function h(x) is a translation of the exponential function,
[tex]g(x) = 2(3)^{x-4}[/tex] is [tex]h(x) = 4(3)^{x-7} - 9\\\\[/tex].
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