Algebra and Trigonometry, 5th Edition

Review Exercises

Determine whether the statement is true or false.

1. 1. If $f(x)=(x+a)(x+b)(x-c)$, then $f(-b)=0$. [4.3]

2. 2. The graph of a rational function never crosses a vertical asymptote. [4.5]

3. 3. For the function $g(x)=x^4-8x^2-9$, the only possible rational zeros are 1, −1, 3, and −3. [4.4]

4. 4. The graph of $P(x)=x^6-x^8$ has at most 6 x-intercepts. [4.2]

5. 5. The domain of the function

   $$f(x)=\frac{x-4}{(x+2)(x-3)}$$

   is $(-\infty ,-2)\cup (3,\infty )$. [4.5]

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic. [4.1]

1. 6. $f(x)=7x^2-5+0.45x^4-3x^3$

2. 7. $h(x)=-25$

3. 8. $g(x)=6-0.5x$

4. 9. $f(x)=\frac{1}{3}{x}^3-2x+3$

Use the leading-term test to describe the end behavior of the ...