Graph the function f(x) = –3x^3 + 9x^2 – 2x + 3 using graphing technology and describe the end behavior
x^3 dominates for end behavior
since the coefficient is -3, the graph descends from (-oo,+oo) and proceeds on out to (+oo,-oo)
solve -x^2+6x-15=0
To graph the function f(x) = –3x^3 + 9x^2 – 2x + 3, you can use graphing technology such as a graphing calculator or a computer graphing software. Here's a step-by-step guide on how to graph this function using a graphing calculator:
1. Turn on your graphing calculator and make sure it is in function graphing mode.
2. Enter the function f(x) = –3x^3 + 9x^2 – 2x + 3 into the function editor.
3. Choose the appropriate window settings for your graph. You may want to set the x-axis and y-axis ranges to include the desired range of values for x and y.
4. Press the graph button or any equivalent button on your calculator to generate the graph of the function.
Once the graph is displayed, you can analyze the end behavior by looking at the behavior of the graph as x approaches positive and negative infinity.
From the graph, you will notice that as x approaches positive infinity, the graph of f(x) decreases without bound, meaning it approaches negative infinity. This indicates a downward trend as x gets larger.
On the other hand, as x approaches negative infinity, the graph of f(x) also decreases without bound, but in the positive direction. This suggests an upward trend as x becomes more negative.
In summary, the end behavior of the function f(x) = –3x^3 + 9x^2 – 2x + 3 can be described as follows: as x approaches positive infinity, the function approaches negative infinity, and as x approaches negative infinity, the function approaches positive infinity.