Which expression represents translating f(x) to the left by 2 units and compressing vertically by a factor of 1/3?

Which expression represents translating f(x) to the left by 2 units and compressing vertically by a factor of 1/3?

• A. g(x) = (1/3) f(x+2)
• B. g(x) = (1/3) f(x-2)
• C. g(x) = 3 f(x+2)
• D. g(x) = (1/3) f(-x+2)

Answer: (A)

Shifting left by 2 is done by replacing x with x + 2 inside the function, giving f(x + 2). Compressing vertically by a factor of 1/3 means multiplying the output by 1/3, yielding (1/3) f(x + 2). So the combined transformation is g(x) = (1/3) f(x + 2). This matches the described changes: left 2 units and vertical compression by 1/3. The other forms either shift in the wrong direction, apply the wrong vertical factor (a stretch rather than a compression), or include a reflection, which isn’t part of the given transformations.

Shifting left by 2 is done by replacing x with x + 2 inside the function, giving f(x + 2). Compressing vertically by a factor of 1/3 means multiplying the output by 1/3, yielding (1/3) f(x + 2). So the combined transformation is g(x) = (1/3) f(x + 2).

This matches the described changes: left 2 units and vertical compression by 1/3. The other forms either shift in the wrong direction, apply the wrong vertical factor (a stretch rather than a compression), or include a reflection, which isn’t part of the given transformations.