9514 1404 393
Answer:
- h = -2; k = 0; vertex = (-2, 0)
- h = 3; k = 0; vertex = (3, 0)
Step-by-step explanation:
Translation of a function to the right h units and up k units is accomplished by ...
g(x) = f(x -h) +k
Here, we have f(x) = |x|, so the translation will be ...
g(x) = |x -h| +k
or ...
y = |x -h| +k
__
The function y = |x| has its vertex at (0, 0), so translation by (h, k) moves the vertex to (0 +h, 0 +k) = (h, k).
__
You will notice that the given equations you are given have no "+k" added on, so k = 0 in both cases. The value of h is the opposite of the constant between the absolute value bars.
1. y = |x +2|
h = -2, k = 0
vertex: (-2, 0)
__
2. y = |x -3|
h = 3, k = 0
vertex: (3, 0)
_____
<em>Additional comment</em>
This is all about <em>matching patterns</em>. You need to be able to identify the variable (x) and what has been added or subtracted to/from it. You need to be able to identify the "parent" function (what you have with nothing added or subtracted), and determine if something is added or subtracted to to/from that. Here, the parent function is |x|. Nothing has been added to the function (outside the absolute value bars), but something has been added to x (inside the absolute value bars).
From the points given we know that the rectangle is 3 points wide and 2 points tall. If we rotate it
around the x axis then we will receive the lying cyllinder which will be 3 points tall and 2 points wide (so its radius is 2/2 = 1 point). Now we can find the surface area of the cyllinder using appropriate formula:
Answer:
4 x 8.5 x 12.5 =425 (multiple hight x width x length)
The volume of the box is 
Area = Length x Width
Given that the area is 30 cm² and Length = 5 cm, find width:
30 = 5 x width
width = 30 ÷ 5 = 6cm
Answer: The width is 6 cm
Answer:
Relateable
Step-by-step explanation:
Obama
