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Brian creates the graph of function g by applying a transformation to function f:

f(x)=4^x+1
g(x)=1/8(4)^x+1
Which transformation did Brian apply?


a vertical compression by a factor of 1/8

a vertical stretch by a factor of 8

a horizontal stretch by a factor of 8

a horizontal compression by a factor of 1/8

Please help worth 20 pts.

2 Answers

6 votes

Answer:

a vertical compression by a factor of
(1)/(8)

Explanation:

Start with the original function
f(x) = 4^x+1.

Apply the vertical compression by multiplying the function by
(1)/(8):


g(x) = ((1)/(8) ) * 4^x+1.

Simplify the expression:


g(x) = (1)/(8) * 4^x * 4^1.

Use the property of exponents
(a^(b+c) = a^b * a^c) to simplify further:


g(x) = (1)/(8) * (4^x * 4).

Simplify the expression inside the parentheses:


g(x) = (1)/(8) * (4^(x+1) ).

User Nicholas Head
by
8.1k points
4 votes

Answer:

a vertical compression by a factor of 1/8

Explanation:

User Qeole
by
7.9k points

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