# Work all math problems and show all work

**Question description**

. Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function. f(x)=4 x^2-5x+4

2. Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function. f(x)= 3-5x+3^2-5x^3

3. Sketch the graph of the function by finding the zeros of the polynomial, f(x)=2 x^3-10 x^2+12x

4. Use synthetic division to divide. (x^3-27x+54)\(x-3)

5. Use the Remainder Theorem and synthetic division to find the function value. g(x)3x^6+3x^4-3x^2+6 g(0)

6. Find all real solutions of the polynomial equation. x^4-4x^3 +12x-9=0

7. The height,h(x),
of a punted rugby ball is given h(x) = 1/64^2 +13/32x +2where*x* is the horizontal distance in feet
from the point where the ball is punted. How far, horizontally, is the ball
from the kicker when it is at its highest point?

8. Find the zeros (if any) of the rational function.g(x) = x^2-16/x-4

9. State the domain of the following function . h(x)= x^2-3/x

10. Simplify fand find any vertical asymptotes ofx=3.

11. Determine the value that the function*f*approaches
as the magnitude of*x* increases.
f(x)=4+ 1/x-2

12. Select the correct graph of the functionf(x)= 6/x+3

13. Select the graph of the rational function. (Plotted additional solution points as needed.) g(x)=1/2-x

14. A biology class performs an experiment comparing the
quantity of food consumed by a certain kind of moth with the quantity supplied.
The model for the experimental data is given by y= 1.577x –
0.0001/6.363x+1, x greater than 0 where*x* is
the quantity (in milligrams) of food supplied and*y* is the quantity (in milligrams) of
food consumed.

At what level of consumption will the moth become
satiated?

15. Select the graph of the exponential function. f(x)5x^-2 +3

16. Select the graph of the function. f(x)=e^5x

17. Select the graph of the function. f(x)=(1/3)^-4

18. Write the exponential equation in logarithmic form. 30^0=1

19. Evaluatef(x) at
the indicated value of*x*. Round your result to three decimal places.
X= -3/2

20. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) log3 9x

21. Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms. Then use a graphing utility to graph the ratio. f(x)=log4^x

22. Solve the exponential equation algebraically. Approximate the result to three decimal places.

23. Solve for x. 1nx-1n5=0

24. The populations (in thousands) of Pittsburgh,
Pennsylvania from 2000 through 2007 can be modeled by p=m2632/1 + 083e ^0.0500 t, where*t* represents the year, witht=0 corresponding to 2000.
Use the model to find the numbers of cell sites in the year 2001.

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