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The exponential function f(x) = 2x undergoes two transformations to
g(x) = 1/3• 2x – 7. How does the graph change? Select all that apply.
A. It is shifted right.
B. It is shifted down.
C. It is flipped over the x-axis.
D. It is vertically compressed.
E. It is vertically stretched.

The Exponential Function Fx 2x Undergoes Two Transformations To Gx 13 2x 7 How Does The Graph Change Select All That Apply A It Is Shifted Right B It Is Shifted class=

Sagot :

MrRoyal

Answer:

Shifting down.

Vertically compressed

Step-by-step explanation:

Given

[tex]f(x) = 2^x[/tex]

[tex]g(x) = \frac{1}{3}(2^x - 7)[/tex]

Required

Determine the translation from f(x) to g(x)

The first translation from f(x) towards g(x) is:

[tex]f(x) = 2^x[/tex]

[tex]f'(x) = 2^x - 7[/tex]

This is derived by:

[tex]f'(x) = f(x) - b[/tex]

Where

[tex]b = 7[/tex]

Notice that, in the above, b (i.e. 7) was subtracted from f(x), this implies that the function shifted down

The next translation that resulted in g(x) is:

[tex]g(x) = \frac{1}{3}(2^x - 7)[/tex]

This is derived by:

[tex]g(x) = a.f'(x)[/tex]

By comparison:

[tex]a = \frac{1}{3}[/tex]

Since the value of a is less than 1, then f'(x) is vertically compressed to give g(x).

Hence, the transformations that apply from f(x) to g(x) are:

  • Shifting down.
  • Vertically compressed

Answer:

shifting down

vertically compressed

Step-by-step explanation:

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