Free Printable Chapter 2: Power, Polynomial, and Rational Functions

1.

Solve the equation $\left(y^4+2y-6\right)^{\frac{1}{4}}=y$

a)

None is correct

b)

3

c)

3, 9

d)

-3

2.

Solve $x=\sqrt{6x-5}$

a)

5

b)

5, 1

c)

5, 2

d)

2

3.

$Graph\ f\left(x\right)=\frac{2}{5}x^3$

a)

b)

c)

d)

4.

Use a graphing calculator to write a polynomial function to model the set of data.

a)

0.9x - 1.3

b)

1.3x - 0.9

c)

0.9x + 1.3

d)

1.3x + 0.9

5.

Graph f(x) = −2(x − 4)⁵ + 1

a)

b)

c)

d)

6.

Describe the end behavior of f(x) = −3x² + 5x³ + 2x using limits. Explain your reasoning using the leading term test.

a)

Because the degree is even and the leading coefficient is positive, limit of f(x) as x approaches -ve inf. equals +ve inf. and limit of f(x) as x approaches +ve inf. equals +ve inf.

b)

Because the degree is odd and the leading coefficient is negative, limit of f(x) as x approaches -ve inf. equals +ve inf. and limit of f(x) as x approaches +ve inf. equals -ve inf.

c)

Because the degree is odd and the leading coefficient is positive, limit of f(x) as x approaches -ve inf. equals -ve inf. and limit of f(x) as x approaches +ve inf. equals +ve inf.

d)

Because the degree is even and the leading coefficient is negative, limit of f(x) as x approaches -ve inf. equals -ve inf. and limit of f(x) as x approaches +ve inf. equals -ve inf.

7.

Use the Remainder Theorem to find the remainder for the division of

(x⁴ - 3x² + 2x - 1) ÷ (x - 1). The remainder is ____.

a)

2

b)

1

c)

0

d)

-1

8.

Factor 5x³ + 26x² + 16x − 32 completely using long division if (x + 4) is a factor.

a)

(x + 4)(x − 2)(5x + 4)

b)

(x + 4)(x − 4)(x + 10)

c)

(x + 4)(x + 2)(5x − 4)

d)

(x + 4)(5x² + 46x + 168)

9.

Divide 5x³ + 23x² − 8x + 8 by x + 5.

a)

$x^2-4x+4-\frac{6}{x+5}$

b)

$5x^2+2x-4-\frac{3}{x+5}$

c)

$5x^2-2x+2-\frac{2}{x+5}$

d)

$5x^2-8x+6-\frac{4}{x+5}$

10.

Write a polynomial equation of least degree with roots -1, 2i, and -2i.

a)

3x+x^2+4x-4=0

b)

$x^3+x^2+4x+4=0$

c)

$x^3-x^2+4x+4=0$

d)

$x^3+x^2-4x+4=0$

11.

Find the rational zeros of the equation 2x⁴ - x³ - 21x² + 9x + 27 = 0.

a)

3, -3, -1, 3/2

b)

3, 1, -1, 3/2

c)

3, -3, -1, 2/3

d)

3, 1, -1, 2/3

12.

Determine between which consecutive integers the real zeros of

f(x) = x⁴ - 4x² + x - 3 are located.

a)

between -4 and -3 and between 3 and 4

b)

between -3 and -2 and between 5 and 6

c)

between -3 and -2 and between 2 and 3

d)

between -2 and -1 and between 2 and 3

13.

List all possible rational zeros f(x) = x³ + 6x² + 3x + 18. Then determine which, if any, are zeros.

a)

\pm18,\ \pm9,\ \pm6,\ \pm3,\ \pm2,\ \pm1;\ -6

b)

18, 9, 6, 3, 2, 1; -6, 2, 9

c)

$\pm18,\ \pm9,\ \pm6,\ \pm3,\ \pm2,\ \pm1;\ -6,\ 2,\ 3$

d)

$\pm9,\ \pm6,\ \pm3,\ \pm2;\ -6,\ 2$

14.

Determine the slant (oblique) asymptote for $f\left(x\right)=\frac{3x^2-x+2}{x-1}$

a)

y = -2x + 3

b)

y = 3x - 2

c)

y= 3x + 2

d)

y = 2x +3

15.

$Graph\ y=\frac{x^2-1}{x-1}$

a)

b)

c)

d)

16.

Determine the asymptotes for the graph of $f\left(x\right)=\frac{2x+1}{x-3}$

a)

a vertical asymptote at x = 3 and a horizontal asymptote at y = 2

b)

none of these

c)

a horizontal asymptote at x = 3 and a vertical asymptote at y = 2

d)

a vertical asymptote at x = -3 and a horizontal asymptote at y = 1

17.

Graph the function $f\left(x\right)=\frac{\left(x+2\right)\left(x-3\right)\left(x+4\right)}{x^2-2x-3}$

a)

b)

c)

d)

18.

$Solve\ \frac{1}{2a}+\frac{3}{4a}<\frac{1}{4}$

a)

a > 0 or 0 < a < 5

b)

a < 0 or 0 < a < 5

c)

0 < a < 5

d)

a < 0 or a > 5

19.

$Solve\ \frac{2x}{x^2-1}>0$

a)

-1 < x < 0 or x > 2

b)

-2 < x < 0 or x > 2

c)

-1 < x < 0 or x > 1

d)

-2 < x < 0 or x < 1

20.

Solve (x − 5)² > 9

a)

\left(-\infty,\ -8\right)\ or\ \left(2,\ \infty\right)

b)

$\left(-\infty,\ \infty\right)$

c)

$\left(-\infty,\ 2\right)\ or\ \left(8,\ \infty\right)$

d)

(2, 8)

Chapter 2: Power, Polynomial, and Rational Functions

Total questions: 20

Worksheet time: 10mins

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