Answer:
- m is shifted to the left 3 units
- m is shifted up 1/2 units
- m is dilated by a scale factor of 2
Step-by-step explanation:
[tex]g(x) =\frac{1}{2} f(x+3)+\frac{1}{2}[/tex]
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 [tex]\frac{1}{2}[/tex]
- Addition of 3 to x
- Addition of [tex]\frac{1}{2}[/tex] 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
