Question

3. Work on this coordinate plane to graph the following functions:
a. Graph the following absolute value function and show your work to determine the vertex:
f(x) = |x + 2|
b. The function g(x) translates f(x) 4 units up. Graph g(x) on the same coordinate plane and write the g(x) function.
c. The function h(x) reflects f(x) over the x-axis. Graph h(x) on the same coordinate plane and write the h(x) function.

Answer 1

@Ultrilliam

Answer 2

@Shadow

Answer 3

i dont understand any of this

Answer 4

Input an x number, get a y, then plot that coordinate.

For example, input 0 for x, get f(x) = y = 2

Your coordinate is (0,2)

Answer 5

okay

Answer 6

Okay but that's just how you would plot points. This question is asking for how you would find the vertex of this absolute value function. The way you would do this is by:

First, setting the right side of the function equal to zero.
\[x + 2 = 0\]
Subtract 2 from both sides
\[x = -2\]
So we have: (-2, ?)

For the y, we input -2 for x, then solve for y.
\[y = |-2 + 2| = 0\]
So our vertex is (-2, 0)

Answer 7

For b, if we want to raise the elevation, we simply need add +4 on the outside, so
\[f(x) = |x+2| + 4\]

Answer 8

If we wish to invert or flip the function over for c, we must add a negative side in front of the absolute value of the function (on variable a).

\[f(x) = -|x + 2|\]

Answer 9

ohh