Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
Question 1:
We are going to add.
1/5 + 1/2
2/10 + 5/10
7/10
Note that we are going DOWN so the number will be negative.
Therefore, the answer is A.) -7/10
Question 2:
We are going to subtract.
4 1/2 - 1 2/3
9/2 - 5/3
27/6 - 10/6
17/6 or 2 5/6
Note that we are still BELOW sea level so the number will be negative.
Therefore, the answer is C.) -2 5/6
Question 3:
We are going to subtract.
2 2/3 - 1 1/5
8/3 - 6/5
40/15 - 18/15
22/15 or 1 7/15
Therefore, the answer is B.) 1 7/15
Best of Luck!
