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Example: f(x) = -3x^2 + 2x^5 - x^3
Description: Look at the the number that has the highest exponent. In this case it would be the third term. Our degree is going to be 5 and our leading coefficient is 2 (term in front of degree). Since the exponent is odd, then the arrows will be going in different directions. Since the leading coefficient is positive, the right side will point up and the left will point down as shown in the third graph.
You get: f(x) = Negative infinity as it approaches negative infinity and f(x) = positive infinity as it approaches positive infinity.
Description: Look at the the number that has the highest exponent. In this case it would be the third term. Our degree is going to be 5 and our leading coefficient is 2 (term in front of degree). Since the exponent is odd, then the arrows will be going in different directions. Since the leading coefficient is positive, the right side will point up and the left will point down as shown in the third graph.
You get: f(x) = Negative infinity as it approaches negative infinity and f(x) = positive infinity as it approaches positive infinity.
ZEROS AND TURNING POINTS OF POLYNOMIAL FUNCTIONS:
Example: f(x) = x^3 + 5x^2 +4x
Description: Look at the highest exponent. That exponent is your degree and your turning point is your degree minus 1.
You get.....Degree: 3 Turning Point: 2
Then you solve for actual real zeros by factoring. You factor by taking out the greatest common factor which is x. You get x(x^2+5x+4).
Then you factor again and get x(x+1)(x+4). Set each equal to zero and you get x=0 x=-1 and x=-4.
Example: f(x) = x^3 + 5x^2 +4x
Description: Look at the highest exponent. That exponent is your degree and your turning point is your degree minus 1.
You get.....Degree: 3 Turning Point: 2
Then you solve for actual real zeros by factoring. You factor by taking out the greatest common factor which is x. You get x(x^2+5x+4).
Then you factor again and get x(x+1)(x+4). Set each equal to zero and you get x=0 x=-1 and x=-4.