High School

Find the x-intercepts (zeros) of the function [tex]f(x) = 4|x + 3| - 8[/tex].

List your solutions as fractions separated by a comma.

The x-intercepts are at [tex]x =[/tex] ___

Answer :

Final answer:

The x-intercepts of the function f(x) = 4|x + 3| - 8 are x = -1 and x = -5. These are found by setting the function equal to zero and solving the resulting equations.

Explanation:

To find the x-intercepts of the function f(x) = 4|x + 3| - 8, you need to solve the equation for when f(x) = 0. This is equivalent to solving 4|x + 3| - 8 = 0.

  1. Add 8 to both sides of the equation: 4|x + 3| = 8.
  2. Divide both sides of the equation by 4: |x + 3| = 2.
  3. Now you'll have two solutions, because the absolute value function creates two solutions. These are x + 3 = 2 and x + 3 = -2.
  4. Solving these equations give the solutions x = -1 and x = -5.

Therefore, the x-intercepts of the function are x = -1 and x = -5.

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