Answer:
The relationship between the graphs of the two functions is "They are reflections of each other across the y-axis" ⇒ B
Step-by-step explanation:
- If the function f(x) reflected across the x-axis, then the new function g(x) = - f(x), which means the signs of the y-coordinates of the points on f(x) are opposite in g(x)
- If the function f(x) reflected across the y-axis, then the new function g(x) = f(-x), which means the signs of the x-coordinates of the points on f(x) are opposite in g(x)
∵ The points on f(x) are (-2, -31), (-1, 0), (1, 2), (2, 33)
∵ The points on g(x) are (2, 3), (1, 0), (-1, 2), (-2, 33)
∵ All x-coordinates on f(x) multiplied by -1 to get the x-coordinates of g(x)
→ By using the 2nd rule above
∴ g(x) is the image of f(x) after reflection across the y-axis
∴ The relationship between the graphs of the two functions is
"They are reflections of each other across the y-axis"
