1.Graph the function f(x) = (x + 3)3 by hand and describe the end behavior
F(x) = Y = 3(x+3) = 3x+9.
Graph the function using the given points:
(-3,0) , (-2,3) ,(0,9) , (1,12).
The graph of this Eq is very odd.
You would expect to get a st. line, but the graph resembles an X-parabola.
If you draw a vertical line through the graph, it will intersect the graph
twice. A function should intersect the line only once. Therefore, the Eq does
not qualify as a function.
3. Graph the function f(x) = –3x3 + 9x2 – 2x + 3 using graphing technology and describe the end behavior.
To graph the function f(x) = (x + 3)^3 by hand, we can follow these steps:
1. Determine the key points:
- Find the y-intercept by substituting x = 0 into the equation:
f(0) = (0 + 3)^3 = 3^3 = 27. So, the y-intercept is (0, 27).
- Find any x-intercepts (if any) by setting f(x) = 0:
(x + 3)^3 = 0. Since a perfect cube cannot be equal to zero, there are no real x-intercepts.
2. Draw the graph:
- Start by plotting the y-intercept (0, 27) on the coordinate plane.
- Since there are no x-intercepts, the graph will not touch or cross the x-axis.
- As x approaches negative infinity (x → -∞), f(x) also approaches negative infinity (f(x) → -∞).
- As x approaches positive infinity (x → +∞), f(x) also approaches positive infinity (f(x) → +∞).
- The graph remains smooth and should resemble a curve rising up from the left and continuing upward indefinitely.
So, the end behavior of the graph is as follows:
- As x approaches negative infinity, f(x) approaches negative infinity.
- As x approaches positive infinity, f(x) approaches positive infinity.
Please note that these instructions assume basic graphing skills and familiarity with plotting points on the coordinate plane.