If you apply the changes below to the absolute value parent function, f(x)=|x|, what is the equation of the new function? shift 8 units left, shift 3 units down.

y= lx+8l -3 is the answer.

Step-by-step explanation:

f(x) = lxl is absolute function if   function is shifted by left of right then its change in x and if  function is changed in up or down then its change in y

so f(x) = lx-hl +k is transformation of f(x) = lxl where h is shifting by right side and  k is shifting to  upward direction.

here its 8 unit left and 3 unit down that is h =-8 and k =-3

so new equation will be

y = lx-(-8)l + (-3)

y = lx+8l -3  is the answer

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

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