The table shows the battery life of four different mobile phones. Mobile Phone Battery Life Phone Battery Life (hours) A 20 B 25 C 10 D 18 If 9.54% of the battery life of each mobile phone is used in a day by a typical user, which mobile phone would use a total of 1.908 hours of battery life in a day? Phone A
Phone B
Phone C
Phone D

Part A: The two types of types of transformation are

1) Rotation of 11.3° about (1, 2)

2) By algebraic transformation

Part B:

Rotation by 11.3° and T(2 - y)×1/2 + x, 0)

Part C: The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)

Step-by-step explanation:

The coordinates through which the linear function f(x) passes = (1. 3) and (3, 13)

The coordinates through which the linear function g(x) passes = (1, 3) and (1, 13)

The equation for f(x) in slope and intercept form. y = m·x + c is given as follows;

The slope, m = (13 - 3)/(3 - 1) = 5

The equation in point and slope form is y - 3 = 5×(x -1)

y = 5·x - 5 + 3 = 5·x - 3

y = 5·x - 3

The equation for g(x) in slope and intercept form. y = m·x + c is given as follows;

The slope, m = (13 - 3)/(1 - 1) = ∞

∴ The equation in point and slope form is x = 1

Therefore, the two equations meet at the point (1, 2)

The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)

2) Another transformation that can be used is to rotate f(x) by the vertex angle as follows

Vertex angle is 90° - tan⁻¹(m) = 90° - tan⁻¹(5) ≈ 11.3°

Rotation of f(x) by 11.3° about (1, 2) gives g(x)