24 in.8- 2xa. Write a function to represent the volume in terms of x.b. What value of x will maximize the volume of water that can be carried by thegutter?Analyze the graph of the given function f as follows:(a) Determine the end behavior of the graph of the function.(b) Find the x- and y-intercepts of the graph.(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.(d) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turningpoints.(f) Find the domain of f. Use the graph to find the(f) Use the graph to determine where f is increasing and where f is decreasing.range of f.39) f(x) = x2(x + 3)%3D39)Form a polynomial f(x) with real coefficients having the given degree and zeros.40) Degree: 4; zeros: -1, 2, and 1 - 2i.40)Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f overnumbers.41) f(x) = 4x3 - 11x2 – 6x + 941)List the potential rational zeros of the polynomial function. Do not find the zeros.

Question
Asked Dec 7, 2019
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F(x)=x2(x+3)

  1. Determine the end behavior of the graph of the function
  2. Find the x- and y- intercepts of the graph
  3. Determine whether the graph crosses or touches the x-axis at each x-intercept.
  4. Use the information obtained in (a)-(e) to draw a complete graoh of f by hand. Label all intercepts and turning points
  5. Find the domain of f. Use the graph to find the range of f.
  6. Use the graph to determine where f is increasing and where f is decreasing.
24 in.
8- 2x
a. Write a function to represent the volume in terms of x.
b. What value of x will maximize the volume of water that can be carried by the
gutter?
Analyze the graph of the given function f as follows:
(a) Determine the end behavior of the graph of the function.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning
points.
(f) Find the domain of f. Use the graph to find the
(f) Use the graph to determine where f is increasing and where f is decreasing.
range of f.
39) f(x) = x2(x + 3)
%3D
39)
Form a polynomial f(x) with real coefficients having the given degree and zeros.
40) Degree: 4; zeros: -1, 2, and 1 - 2i.
40)
Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over
numbers.
41) f(x) = 4x3 - 11x2 – 6x + 9
41)
List the potential rational zeros of the polynomial function. Do not find the zeros.
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24 in. 8- 2x a. Write a function to represent the volume in terms of x. b. What value of x will maximize the volume of water that can be carried by the gutter? Analyze the graph of the given function f as follows: (a) Determine the end behavior of the graph of the function. (b) Find the x- and y-intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points. (f) Find the domain of f. Use the graph to find the (f) Use the graph to determine where f is increasing and where f is decreasing. range of f. 39) f(x) = x2(x + 3) %3D 39) Form a polynomial f(x) with real coefficients having the given degree and zeros. 40) Degree: 4; zeros: -1, 2, and 1 - 2i. 40) Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over numbers. 41) f(x) = 4x3 - 11x2 – 6x + 9 41) List the potential rational zeros of the polynomial function. Do not find the zeros.

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Expert Answer

Step 1

 The given function is

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f(x) = y= x²(x + 3)

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Step 2

(a)

Observe that for large positive values of variable x, the value of the function is a large positive number and further increase in the value of the variable will only increase value of the function. Thus the right end behaviour of the function is that it tends to infinity as input x tends to infinity.

Similarly observe that for large negative values of variable x, the value of the function is a large negative number and further decrease in the value of the variable will only decrease value of the function. Thus the left end behaviour of the function is that it tends to negative infinity as input x tends to negative infinity.

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If x→o then f (x)→∞ If x→-o then f (x) - →-∞

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Step 3

A y-intercept can be found by finding f(0) and an x-int...

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f(0) = 0° (0 +3) = 3 → y-intercept = 3 f (x)= y= x' (x +3)= 0 →x= -3 or x=0 →x-intercept = -3,0

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