Question

Pls help asap!! pic is shown

Answer 1

The points (-5, 1), (-2, 4), (2, 4), and (-5, 1) gives the piecewise defined function as the second option;

g(x) = x + 6, when x < -2

g(x) = x², when -2 ≤ x < 2

g(x) = 6 - x, when x ≥ 2

How can the correct piecewise defined function be found?

Parts of the function are:

x < -2

Slope = (4-1)/(-2-(-5)) = 1

Equation is: g(x) - 4 = x - (-2)

g(x) - 4 = x + 2

g(x) = x + 2 + 4 = x + 6

• g(x) = x + 6

In the region, -2 ≤ x < 2, points on the graph are;

(-2, 4), (0, 0), (2, 4)

The above points corresponds with the function;

• g(x) = x²

In the region x ≥ 2, we have;

Slope = -1

Equation is: g(x) - 4 = -1×(x - 2) = 2 - x

Therefore;

g(x) = 4+2 - x = 6 - x

• g(x) = 6 - x

The rule for the piecewise defined function is therefore;

• g(x) = x + 6, when x < -2
• g(x) = x², when -2 ≤ x < 2
• g(x) = 6 - x, when x ≥ 2

The correct option is therefore the second option;

Learn more about piecewise defined functions here:

brainly.com/question/11207865

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