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Find the 
y-coordinate of the 
y-intercept of the polynomial function defined below.

f(x)=9x-4x^(2)+9x^(3)-3
Answer:

Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=9x4x2+9x33 f(x)=9 x-4 x^{2}+9 x^{3}-3 \newlineAnswer:

Full solution

Q. Find the y y -coordinate of the y y -intercept of the polynomial function defined below.\newlinef(x)=9x4x2+9x33 f(x)=9 x-4 x^{2}+9 x^{3}-3 \newlineAnswer:
  1. Evaluate at x=0x = 0: To find the yy-coordinate of the yy-intercept of the function f(x)f(x), we need to evaluate f(x)f(x) at x=0x = 0, because the yy-intercept occurs where the graph of the function crosses the yy-axis, and this happens at x=0x = 0.
  2. Substitute into f(x)f(x): Substitute x=0x = 0 into the polynomial function f(x)=9x4x2+9x33f(x) = 9x - 4x^2 + 9x^3 - 3.f(0)=9(0)4(0)2+9(0)33f(0) = 9(0) - 4(0)^2 + 9(0)^3 - 3
  3. Simplify the expression: Simplify the expression by performing the operations. f(0)=00+03f(0) = 0 - 0 + 0 - 3
  4. Final result: The result of the simplification gives us the y-coordinate of the y-intercept. \newlinef(0)=3f(0) = -3

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