Answers:
y = f(-x) + 3
(x, y) = (x+5, y - 8)
Translate the figure 3 unit to the right and reflect across the x-axis
Explanation:
A transformation will result in a congruent figure if it just a translation, rotation, or a reflection of the original function.
For the first answer, we get:
if y = f(-x), then y is a reflection over the y-axis of f(x)
if y = f(x) + c, then y is a translation of c units up
It means that y = f(-x) + 3 is a reflection over the y-axis and a otranslationf 3 units up. So, this is a correct answer
For the second answer, we get:
if y = cf(x), then y is a vertical stretch of f(x) by a factor of c
if y = f(x+c), then y is a translation of c unit to the left
It means that y = 3f(x+4) is a translation of 4 units to the left and a vertical stretch of f(x). Since it is a vertical stretch, this is not a correct answer.
For the third answer:
(x, y) -> (12x, y) is a transformation where the value of x is changed by a factor of 12, so this is not a correct answer.
For the 4th answer:
(x, y) -> (x + 5, y - 8) is a translation of 5 units to the right and 8 units down. It means that this is a correct answer.
For the 5th answer:
This answer just involves translation and reflection. It means that this is a correct answer.
For the 6th answer:
This answer has a rotation and a dilatation. Since it involves a dilation by a factor of 4, this is not a correct answer.
