pre cal semester one exam

6. The polynomial function p is given by p(x) = -x(x + 3)(x - 2)^2

A, starts from bottom curves up, back down, then back up

8. Let f(x) = x^2 - x - 6 and g(x) = 2x^2 + x - 6. What are all the intervals on which g(x) _> f(x) ?

(-oo, -2) U [0, oo)

2. The function g is a polynomial with the following end behavior: lim g(x) =oo and lim g(x) = -oo. Which of the following could be an expression for g(x)?

-3x^5 + 4x^2 + 1

4. The figure aboce shows the graph of a function h. For how many values of b does the function h have an average rate of change of 1/2 over the interval from x = -2 to x = b

2

T12. he graph of f is shown above the six points A,B,C,D,E and F labeled. What are all the points where the graph of f has a local maximun?

A,C, and E

14. The function r is given by r(x) = x^2 + 2x - 24/x^3 + 8x^2 +12x. What is the domain of r?

All real numbers x where x /= -6, 0, 2, and 4

1. the graph of function "k" is shown in the figure above. Which of the following best descibes the behavior of the graph of "k" from point A to point B?

The graph of "k" is increasing and concave down

9. The rational function r is given by r(x) = 2x^2 - 3x + 7/ x - 4. Which of the following statements about r is correct?

The graph of r has a slant asymptote of y = 2x + 5

13. Let g be a polynomial function whose graph has a point of inflection at x = 3. Which of the following statements about g must be true?

The graph of the rate of change of g has a relative extremum at x = 3

10. The tabke above shows values for the polynomial function g at selected values of x. Which of the following claim and expalntation statements could be true about g?

The least possible degee of g is four

5. The table shows values for a function f at selected values of x. Which of the following statements about f best fits these data?

f is best modeled by a quadratic function because the change in the average rates of change over consecutive equal-lenght input-value intervals is constant.

3. The graph of function f has a hole at x = -1 and a verticle asymptote at x = 3. Which of the following functions could be f(x) ?

f(x) = x^2 + 3x + 2/ x^2 - 2x - 3

7. The polynomial h is given by h(x) = x^2(x^2 = 1)

h has exactly one distinct real zero and two non real zeros

11. The functions m and n are defined for all real numbers. In the xy plane, the graph of n is constructed by applying three transformations to the grpah of m in this order: a horizontal dilation by a factor of 2, a horizontal tanslation of 4 units, and a verticle translation of -8 units. Which of the following is the correct transformation that maps the grpah of m to n in the same xy plane?

n(x) = m(1/2(x - 4)) -8