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A function is shown: 
f(x)=36x^(2)-1.
Choose the equivalent function that best shows the 
x-intercepts on the graph. (1 point)

f(x)=18(x^(2)-1)

f(x)=(18 x+1)(18 x-1)

f(x)=6(x^(2)+1)

f(x)=(6x+1)(6x-1)

A function is shown: f(x)=36x21 f(x)=36 x^{2}-1 .\newlineChoose the equivalent function that best shows the x x -intercepts on the graph. (11 point)\newlinef(x)=18(x21) f(x)=18\left(x^{2}-1\right) \newlinef(x)=(18x+1)(18x1) f(x)=(18 x+1)(18 x-1) \newlinef(x)=6(x2+1) f(x)=6\left(x^{2}+1\right) \newlinef(x)=(6x+1)(6x1) f(x)=(6 x+1)(6 x-1)

Full solution

Q. A function is shown: f(x)=36x21 f(x)=36 x^{2}-1 .\newlineChoose the equivalent function that best shows the x x -intercepts on the graph. (11 point)\newlinef(x)=18(x21) f(x)=18\left(x^{2}-1\right) \newlinef(x)=(18x+1)(18x1) f(x)=(18 x+1)(18 x-1) \newlinef(x)=6(x2+1) f(x)=6\left(x^{2}+1\right) \newlinef(x)=(6x+1)(6x1) f(x)=(6 x+1)(6 x-1)
  1. Factor using difference of squares: Factor the equation using the difference of squares formula, which is a2b2=(a+b)(ab)a^2 - b^2 = (a + b)(a - b). \newlinef(x)=36x21f(x) = 36x^2 - 1 can be written as f(x)=(6x)2(1)2f(x) = (6x)^2 - (1)^2.
  2. Apply formula: Apply the difference of squares formula to get f(x)=(6x+1)(6x1)f(x) = (6x + 1)(6x - 1).\newlineThis shows the x-intercepts at x=16x = -\frac{1}{6} and x=16x = \frac{1}{6}.
  3. Check answer choices: Check the answer choices to find the equivalent function.\newlineThe correct choice is f(x)=(6x+1)(6x1)f(x) = (6x + 1)(6x - 1).

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