Write an equation that represents a vertical translation 7 units down of the graph of g(x)=|x|.

g(x) = |x| - 7

Step-by-step explanation:

Given the parent function, g(x) = |x|, and its vertex at (0, 0):

Vertical translations: g(x) = |x| + k where:

k > 0, shifts up |k | units

k < 0, shifts down |k | units

Thus, a vertical translation of the parent graph can be represented with the following absolute value function:

g(x) = |x| - 7

where the vertex occurs at point, (0, -7).

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pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.