. Which equation represents the function graphed on the coordinate plane? g(x)=|x+4|-2 g(x)=|x-4|-2 g(x)=|x-2|-4 g(x)=|x-2|+4 Mark this and return

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. Which equation represents the function graphed on the coordinate plane? g(x)=|x+4|-2 g(x)=|x-4|-2 g(x)=|x-2|-4 g(x)=|x-2|+4 Mark this and return

  1. Check all equations that are equivalent.

a=180(n-2)
n=(a)/(180)+1
n=(a)/(180)+2
n=(a+360)/(180)

The Correct Answer and Explanation is:

Let’s work through both questions one by one:

Question 1: Which equation represents the function graphed on the coordinate plane?

Since you did not provide an image of the graph, I will explain how to identify the correct equation if you’re looking at a graph of an absolute value function.

An absolute value function is in the general form: g(x)=∣x−h∣+kg(x) = |x – h| + k

Where:

  • hh determines the horizontal shift (left or right),
  • kk determines the vertical shift (up or down),
  • The vertex of the V-shaped graph is located at the point (h,k)(h, k).

To determine the correct equation:

  • Find the vertex on the graph. This is the point where the “V” changes direction.
  • Plug that vertex into the standard form g(x)=∣x−h∣+kg(x) = |x – h| + k, adjusting signs accordingly.

Let’s look at the answer choices:

  1. g(x) = |x + 4| – 2 → Vertex is at (-4, -2)
  2. g(x) = |x – 4| – 2 → Vertex is at (4, -2)
  3. g(x) = |x – 2| – 4 → Vertex is at (2, -4)
  4. g(x) = |x – 2| + 4 → Vertex is at (2, 4)

So, find the vertex on the graph and match it with the equation’s vertex. For example, if the vertex is at (4, -2), then the correct answer is g(x) = |x – 4| – 2.

Question 2: Check all equations that are equivalent.

Given:

  1. a=180(n−2)a = 180(n – 2) — This is the formula for the sum of interior angles in a polygon with nn sides.
  2. n=a180+1n = \frac{a}{180} + 1
  3. n=a180+2n = \frac{a}{180} + 2
  4. n=a+360180n = \frac{a + 360}{180}

We will check which equations are equivalent to the first one.

Step-by-step:

Start with: a=180(n−2)a = 180(n – 2)

Now solve for nn: a180=n−2⇒n=a180+2\frac{a}{180} = n – 2 \Rightarrow n = \frac{a}{180} + 2

So the correct rearranged version of the formula is:

n = (a/180) + 2 → This one IS equivalent.

Now test each:

  • n=a180+2\boxed{n = \frac{a}{180} + 2} → ✅ Correct
  • n=a180+1n = \frac{a}{180} + 1 → ❌ Incorrect (off by 1)
  • n=a+360180n = \frac{a + 360}{180} → Check: a+360180=180(n−2)+360180=180n−360+360180=180n180=n\frac{a + 360}{180} = \frac{180(n – 2) + 360}{180} = \frac{180n – 360 + 360}{180} = \frac{180n}{180} = n So this is also correct → ✅

✅ Correct equivalent equations:

  • n=a180+2n = \frac{a}{180} + 2
  • n=a+360180n = \frac{a + 360}{180}

✅ Final Answers:

Question 1: Choose the equation whose vertex matches the graph. Use the vertex to determine the correct option.

Question 2: The equivalent equations are:

  • n=a180+2n = \frac{a}{180} + 2
  • n=a+360180n = \frac{a + 360}{180}

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