Question: 1. Given the polynomial function f(x) = ax ^ 3 - 6x ^ 2 + 22x + b , f(- 2) = - 24 ,

1. Given the polynomial function f(x) = ax ^ 3 - 6x ^ 2 + 22x + b , f(- 2) = - 24 , and the y-intercept is 12, determine the equation of the polynomial. 2. Consider the inequality - (1 + x ^ 2) ^ 5 (14 - x) ^ 2 - 1 > 0. Explain for what value (S) for x will the inequality be true? Justify your reasoning 3. As the water drains from a bathtub, the volume, V, in litres, of water remaining in the bathtub after t minutes can be modelled by the function: V(t) = 1.75 (5 - t) ^ 3 , where {0 t 5} a) Determine the rate of change over the first 3 minutes of the water draining. b) Determine the rate of change at the 4 minute mark. 4. Algebraically, determine whether f(x) = 2x (x - 4) is even, odd, or neither

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

emet To earn full This is an evaluation that must be completed on your own with no help from tutors friends marks you must justify your solution Include the following as needed Show diagram Define...

. Use the pair of the pair of functions to find f (g (x)) and g (f (x)) . Simplify the answer f (x) = sqrt x+2, g (x) = x^2+5 f (g (x)). = g (f (x)). = show how you arrive at the answer 2. The graph...

1. Given the rational function f (x) = -2x-15 [4] x- + 4x+3' a) State the equation(s) of all asymptote(s) and/or the coordinates of point(s) of discontinuities. 10 7 0 00 10 -8 - 6 -4 -2 2 4 6 8 10...

Odd degree power functions are always symmetrical about the y-axis. * 1 point 'I point 1 point Odd-degree polynomial functions have at least one x-intercept * 1 point Which of the following graphs...

(8 pts) 1. For the polynomial function f (x) =-(x+5) (x-2), determine its intercepts with the axes, and its end behavior. Sketch the graph of this function. (a) x-intercepts: (b) y-intercept: (c) End...

Example 18 Prove that the function defined by f x tan x is a continuous function Solution The function f x tan x sin x COS X TU that cos x 0 i e x 2n 1 2 We have just proved that both sine and cosine...

1. Using the limit definition of derivative, find f (3) for the function f (x) = x3 + 17x - 12x + 2 2. Find the slope of the secant line between the values 3 and 4 for the function f (x) = ax 3....

1. State the degree and the leading coefficient of each polynomial (K) a. y = 2x3+ 3x - 1 b. y = 21 - 2x + 4x2 - 6x3 2. Match each function to its end behavior. (K) y = 3x7 y= -=x3 y = 2x4 y =...

For 2008, Orchard Corporation reported after-tax net income of $5,800,000. During the year, the number of shares of stock outstanding remained constant at 10,000 of $100 par, 9 percent preferred...

A Carnot engine has an efficiency of 22.0%. It operates between constant-temperature reservoirs differing in temperature by 75.0 Co. What is the temperature of the (a) Lower temperature and (b)...

Question 1 6 1 pts The amount of the death benefit under an Option A universal life insurance policy is always Increasing Decreasing Level Constantly fluctuating

What could happen if the system solution acts differently than what is shown in the UML activity diagram.