Question

A point (1, 1) lies on the graph of a function f(x). After a sequence of three transformations, the point (1, 1) is mapped to (2, -7). Express the transformed function g(x) in terms of f(x).

a) g(x)=f(x)−8x

b) g(x)=f(x)−2x−8

c) g(x)=f(x)+2x−8

d) g(x)=f(x)+8x

Answer 1

To express the transformed function g(x) in terms of f(x), we need to determine the sequence of three transformations that map the point (1, 1) to (2, -7). The transformed function g(x) can be expressed as g(x) = f(x + 1) * -7.

Step-by-step explanation:

To express the transformed function g(x) in terms of f(x), we need to determine the sequence of three transformations that map the point (1, 1) to (2, -7). Let's assume the three transformations are: translation, dilation, and reflection.

Translation: In this case, the point (1, 1) is mapped to (1 + a, 1), where 'a' represents the amount of horizontal translation. Since the point (1, 1) is mapped to (2, -7), we can determine that 'a' is equal to 1. So the translated point is (2, 1).

Dilation: In this case, the point (2, 1) is mapped to (b * 2, b * 1), where 'b' represents the scale factor. Since the point (2, 1) is mapped to (2 * 1, -7), we can determine that 'b' is equal to -7. So the dilated point is (2, -7).

Reflection: In this case, the point (2, -7) is mapped to (2, -7). This means there is no reflection taking place.

Therefore, the transformed function g(x) can be expressed as g(x) = f(x + 1) * -7.