Given a function f(x) we translate the function:
• a units horizontally (a > 0 to the right, a < 0 to the left),
,• b units vertically (b > 0 up, b < 0 down),
by the transformation:
In this case, we have:
Comparing f(x) and g(x) with the general transformation above, we see that the graph of g(x) is the graph of f(x) translated:
• a = 2 units to the right,
,• b = 4 units up.
Translating the graph of f(x), we get:
AnswerThe translated graph is the graph in red:
Answer:
Carlos is incorrect.
Step-by-step explanation:
We have been given that a line through the origin has a slope of . Carlos thinks the slope of a perpendicular line at the origin will be 3.
We know that the slope of a perpendicular line to a given line is always negative reciprocal of the slope of the given line.
The slope of the perpendicular line at the origin will be negative reciprocal of .
Let us find negative reciprocal of as:
Since the slope of a perpendicular line at the origin is , therefore, Carlos is incorrect.