Question

The function h(x) is a translation of the exponential function g(x) = 2(3)x − 4. 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? Question 11 options: A) h(x) = 4(3)x − 7 + 9 B) h(x) = 4(3)x − 9 + 7 C) h(x) = 4(3)x – 7 + 7 D) h(x) = 4(3)x + 7 − 9

Answer 1

The function h(x) is a translation of the exponential function $g(x) = 2(3)^{x - 4}$ , is  $h(x) = 4(3)^{x + 7} - 9$

What are exponential functions?

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

There usual form is specified below. They are written in several such equivalent forms.

The function h(x) is a translation of the exponential function given as

$g(x) = 2(3)^{x - 4}$

We have to determine, the h(x) if the translation is a vertical stretch by a factor of 2, a vertical shift upward of 9 units, and a horizontal shift to the right 7 units.

The function h(x) is vertically stretched by 2.

  $h(x) = 2 (2(3)^{x - 4})\\\\h(x) = 4((3)^{x - 4})$      

Vertically shift upward by 9,

$h(x) = 4((3)^{x - 4})\\\\h(x) = 4((3)^{x - 4})- 9$                    

And a horizontal shift to the right 7 units,

$h(x) = 4((3)^{x - 7})- 9$                    

The function h(x) is a translation of the exponential function $g(x) = 2(3)^{x - 4}$ , is  $h(x) = 4(3)^{x + 7} - 9$

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