Question

Start with f(x)=x^2. Shift it 6 to the right, reflect it vertically, compress it vertically by 0.5, and then shift it up by 25 to get R(x) (revenue for selling x items). Give the final equation of R(x).

a) R(x)=-0.5(x+6)^2 +25
b) R(x)=-0.5(x-6)^2 +25
c) R(x)=0.5(-x^2 +6) + 25
d) R(x)=-0.5(x-6) +25
e) R(x)=-0.5(x^2+6) + 25

Answer 1

The function f(x)=x^2 is transformed through several steps to become R(x), with the correct final equation being R(x)=-0.5(x-6)^2 + 25.

Step-by-step explanation:

The student is asking how to transform the function f(x)=x^2 to find the final equation of R(x) after applying several transformations. Starting with f(x)=x^2, we first shift it 6 units to the right, which gives us f(x)=(x-6)^2. Reflecting it vertically means we multiply the entire function by -1, so f(x)=-1(x-6)^2. Next, we compress it vertically by 0.5, resulting in f(x)=-0.5(x-6)^2. Finally, we shift the function up by 25 units to get R(x)=-0.5(x-6)^2 + 25. Therefore, the correct final equation for R(x) is b) R(x)=-0.5(x-6)^2 + 25.