Question

Start with f(x)=x^2 Shift it 5 to the right, reflect it vertically, compress it vertically by a

factor of 0.2, and then shift it up by 20 to get R(x) (revenue for selling x items).
a) f(x)=-0.2(x+5) + 20
b) f(x)=-0.2(x- 5) + 20
c) f(x) = 0.2(-x? +5) +20
d) f(x)=-0.2(x+5)2 + 20
e) f(x)=-0.2(x - 5)2 + 20

Answer 1

After performing the transformations, the correct form of the function R(x) is f(x)=-0.2(x-5)^2+20. Option e is correct.

Step-by-step explanation:

To find the final form of the function R(x) after the series of transformations, we must apply each transformation step by step to the original function f(x) = x2.

Shift 5 units to the right:

f(x) = (x - 5)2.

Reflect vertically:

f(x) = -(x - 5)^2.

Compress vertically by a factor of 0.2:

f(x) = -0.2(x - 5)^2.

Shift up by 20:

f(x) = -0.2(x - 5)^2 + 20.

After applying all these transformations, the correct function for R(x) is f(x) = -0.2(x - 5)2 + 20.

Hence, option e is correct.