Question

Line m is represented by the function f(x)= 1/3x + 5/2.

After transformation, the image, line m’, is represented by the functions g(x)= 1/2f(x+3) + 1/2. Which statement below describe the transformation from m to m’? Select all that apply.

m is dilated by a scale factor of 1/3

m is shifted to the left 3 units

m is sifted to the left 5/2 units

m is shifted up 1/2 units

m is dilated by a scale factor of 2

Answer 1

I have tried the answer given on Math Nation and it told me the answer was wrong. The answers are:

• m is shifted to the left 3 units
• m is shifted up
  `(1)/(2)` units.

Explanation:

Answer 2

• m is shifted to the left 3 units
• m is shifted up 1/2 units
• m is dilated by a scale factor of 2

Explanation:

`g(x) =(1)/(2) f(x+3)+(1)/(2)`

Following changes are made in f(x) i.e. Line m to get g(x) i.e. the Line m'

• Multiplication of f(x) by
  `(1)/(2)`
• Addition of 3 to x
• Addition of
  `(1)/(2)` to function value

1) Multiplication of f(x) by 1/2

Multiplying the function by a number indicates dilation. So this means Line m is dilated by a factor of 2. The dilation in this case is compression. So the function is being compressed by a factor of 2.

2) Addition of 3 to x

Addition of a value directly to x shifts it horizontally towards left. So Line m is shifted 3 units to left.

3) Addition of 1/2 to function value

Addition of a number to function value indicates vertical upward shift. So the Line m is shifted up by 1/2 units

Therefore, the correct answers are:

• m is shifted to the left 3 units
• m is shifted up 1/2 units
• m is dilated by a scale factor of 2