Students match verbal transformations of f(x)=3x-7 to function rules: reflection & left 7 -> g(x)=-3x-7, vertical stretch 4 & up 9 -> g(x)=12x+9, vertical stretch 2 & up 5 -> g(x)=6x+5, up 6 & right 2 -> g(x)=3x-1.
The image you sent shows a matching activity where students need to match verbal descriptions of transformations of a function to the correct function rule. The original function is f(x) = 3x - 7.
Here's how to match each description to its corresponding function rule:
1. The function f reflected about the y-axis and translated 7 units left:
Reflecting about the y-axis means multiplying by -1.
Translating 7 units left means adding 7 to x.
Combining these transformations, the function rule is g(x) = -3x - 7.
2. The function f stretched vertically by a factor of 4 and translated up by 9 units:
Stretching vertically by a factor of 4 means multiplying by 4.
Translating up by 9 units means adding 9.
Combining these transformations, the function rule is g(x) = 12x + 9.
3. The function f stretched vertically by a factor of 2 and translated up by 5 units:
Stretching vertically by a factor of 2 means multiplying by 2.
Translating up by 5 units means adding 5.
Combining these transformations, the function rule is g(x) = 6x + 5.
4. The function f translated 6 units up and 2 units right:
Translating up 6 units means adding 6.
Translating 2 units right means replacing x with x - 2 (because moving right is like subtracting from x).
Combining these transformations, the function rule is g(x) = 3x - 1.
Therefore, the matches are:
The function f reflected about the y-axis and translated 7 units left: g(x) = -3x - 7
The function f stretched vertically by a factor of 4 and translated up by 9 units: g(x) = 12x + 9
The function f stretched vertically by a factor of 2 and translated up by 5 units: g(x) = 6x + 5
The function f translated 6 units up and 2 units right: g(x) = 3x - 1