6.02 Algebra 2
1. Graph the function f(x) = (x + 3)3 by hand and describe the end behavior. (1 point)
The Function is cubic so it ends in opposite directions, the left side will go down and the right side up since the first coefficient is positive.
2. Graph the function f(x) = –x4 – 4 by hand and describe the end behavior. (1 point)
The function is quartic so the left and right end will continue in the same direction, the lead coefficient is negative so both sides will go down.
3. Graph the function f(x) = –3x3 + 9x2 – 2x + 3 using graphing technology and describe the end behavior. (1 point)
The function is cubic so the left and right ends will not continue in the same direction, since the first coefficient is negative the left side will go up and the right down.
4. Graph the function f(x) = x4 – 7x3 + 12x2 + 4x – 12 using graphing technology and describe the end behavior. (1 point)
The function is quartic meaning the two ends will go in the same direction, the first coefficient is even so the left and right end will go up.
5. Without using technology, describe the end behavior of f(x) = –3x38 + 7x3 – 12x + 13. (1 point)
The first exponent is even so the left and right side will go in the same direction, the lead coefficient is negative so they will both go down.
6. Using complete sentences, explain how to find the zeros of the function f(x) = 2x3 – 9x + 3. (2 points) The last number shows where to find the zero, in this case the coordinate would be (0,3)
The Function is cubic so it ends in opposite directions, the left side will go down and the right side up since the first coefficient is positive.
2. Graph the function f(x) = –x4 – 4 by hand and describe the end behavior. (1 point)
The function is quartic so the left and right end will continue in the same direction, the lead coefficient is negative so both sides will go down.
3. Graph the function f(x) = –3x3 + 9x2 – 2x + 3 using graphing technology and describe the end behavior. (1 point)
The function is cubic so the left and right ends will not continue in the same direction, since the first coefficient is negative the left side will go up and the right down.
4. Graph the function f(x) = x4 – 7x3 + 12x2 + 4x – 12 using graphing technology and describe the end behavior. (1 point)
The function is quartic meaning the two ends will go in the same direction, the first coefficient is even so the left and right end will go up.
5. Without using technology, describe the end behavior of f(x) = –3x38 + 7x3 – 12x + 13. (1 point)
The first exponent is even so the left and right side will go in the same direction, the lead coefficient is negative so they will both go down.
6. Using complete sentences, explain how to find the zeros of the function f(x) = 2x3 – 9x + 3. (2 points) The last number shows where to find the zero, in this case the coordinate would be (0,3)