Fall 2022 Final Exam Review

7. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. f(x) = 5x + 6x^4

Yes; degree 4

9. Determine the domain and the range of the function. f(x) = -x^2 - 10x

domain: all real numbers range: {y|y less than or equal to 25}

10. Form a polynomial whose zeros and degree are given. Zeros: -3, -5, 5; degree 3

f(x) = x^3 - 25x + 3x^2 - 75 for a = 1

5. Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

function domain:{x|-pi less than or equal to x less than or equal to pi} range:{y|-1 less than or equal to y less than or equal to 1} intercepts:(-pi,0),(0,0),(pi,0) symmetry: origin

4. The graph of a function f is given. Use the graph to answer the question. Is f(80) positive or negative?

positive

8. Graph the function using its vertex, axis of symmetry, and intercepts. f(x) = -x^2 - 2x

vertex (-1, 1) intercepts (0, 0), (-2, 0)

13. Find the vertical asymptotes of the rational function. x+8/x^2-36

x = -6, x = 6

14. Give the equation of the horizontal asymptote, if any, of the function. T(x)=7x^2-6x-3/5x^2-5x+3

y =7/5

12. Find the domain of the rational function. R(x)=x+6/x^2-9

{x|x doesn't equal -3,x doesn't equal 3}

3. Find the domain of the function. x/sqrtx-5

{x|x>5}

6. Find the vertex and axis of symmetry of the graph of the function. f(x) = 3x^2 + 6x + 4

(-1, 1) ; x = -1

15. Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x) = 5x^3 - 22x^2 - 17x + 10

-1,2/5 , 5; f(x) = (5x - 2)(x - 5)(x + 1)

11. For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x) = 3(x + 2)(x - 4)^3

-2, multiplicity 1, crosses x-axis; 4, multiplicity 3, crosses x-axis

1. Find the value for the function. Find f(-2) when f(x) = x^2 + 3x - 2.

-4

2. Find the value for the function. Find f(x + h) when f(x) = 8x+5/3x+2.

8x+8h+5/3x+3h+2