Problem

Find the holes in the graph of the function f(x)=x2−9x−3.

Answer

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Answer

Step 4: To find the y-coordinate of the hole, substitute x=3 into the simplified function f(x)=x+3 to get f(3)=3+3=6.

Steps

Step 1 ：Step 1: Simplify the function, f(x)=x2−9x−3, by factoring the numerator to get f(x)=(x−3)(x+3)x−3.

Step 2 ：Step 2: Cancel out the common factor (x−3) in the numerator and the denominator to get f(x)=x+3.

Step 3 ：Step 3: Determine the value of x that makes the original denominator zero since this value of x will be a hole in the graph. In this case, x−3=0 implies that x=3 is a hole.

Step 4 ：Step 4: To find the y-coordinate of the hole, substitute x=3 into the simplified function f(x)=x+3 to get f(3)=3+3=6.

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