find the following for the function f(x)=(x+3)^2(x-1)^2
a.) find the x and y intercept of the polynomial function f.
b.)find the power function that the graph of f ressembles for large values of lxl.
c.)determine the maximum number of turning pointsof the graph of f.
d.) determine the behavior of the graph near each x-intercept.
I don't get this at all, can someone please help me?!?!
You can visit
http://rechneronline.de/function-graphs/
to see the graph.
Change the range to -5 - 25 to scale the graph and make it more useful.
Enter (x+3)^2 * (x-1)^2 for the first graph and (x+1)^4 for the second.
That should enable you to answer all the questions and understand the concepts.
Sure, I can help you understand how to answer these questions.
a.) To find the x-intercepts of a function, we set f(x) = 0 and solve for x. In this case, the x-intercepts occur when the function equals zero. So, we can set (x + 3)^2(x - 1)^2 = 0 and solve for x. This equation can be factored as (x + 3)(x + 3)(x - 1)(x - 1) = 0. From this, we can see that the x-intercepts occur at x = -3 and x = 1. To find the y-intercept, we set x = 0 in the function f(x) and evaluate it. In this case, f(0) = (0 + 3)^2(0 - 1)^2 = 9 * 1 = 9. So, the y-intercept is 9.
b.) To find the power function that the graph of f resembles for large values of lxl (x approaches positive or negative infinity), we look at the highest power of x in the function. In this case, the highest power is x^2. Therefore, the graph of f resembles a power function (or a polynomial function) of degree 2 for large values of lxl.
c.) The maximum number of turning points of a graph is determined by the degree of the function minus one. In this case, the function f(x) = (x+3)^2(x-1)^2 is a quartic function, as it has a degree of 4. So, the maximum number of turning points would be 4 - 1 = 3.
d.) To determine the behavior of the graph near each x-intercept, we can look at the factors of the function. In this case, we have (x + 3)^2 and (x - 1)^2.
- At x = -3, we have a double root, meaning the graph touches the x-axis but does not cross it. The multiplicity of 2 indicates that the graph has a "bounce" at that point.
- At x = 1, we also have a double root, so the graph touches the x-axis but does not cross it again.
I hope this helps! Let me know if you have any further questions.