Free Printable Pre Calculus S2 Final Exam

1.

Choose the end behavior for this polynomial function.

$f(x)=2x^5-3x^2+4x-10$

a)

$\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty;\ \lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$

b)

$\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty;\ \lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$

c)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty;\ \lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$

d)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty;\ \lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$

2.

What are the zeros and their multiplicities of the polynomial graphed?

a)

-6 (multiplicity of 1)

-5 (multiplicity of 2)

-2 (multiplicity of 2)

1 (multiplicity of 1)

b)

-6 (multiplicity of 2)

-5 (multiplicity of 1)

-2 (multiplicity of 1)

1 (multiplicity of 2)

c)

6 (multiplicity of 1)

5 (multiplicity of 2)

2 (multiplicity of 2)

-1 (multiplicity of 1)

d)

6 (multiplicity of 2)

5 (multiplicity of 1)

2 (multiplicity of 1)

-1 (multiplicity of 2)

3.

Using the Rational Zeros Theorem, which is the complete list of the possible rational zeros for the polynomial function?

$f\left(x\right)=5x^4+8x^2-7x+15$

a)

$\pm1,\ \pm3,\ \pm5,\ \pm15$

b)

$\pm\frac{1}{5},\ \pm1,\ \pm\frac{3}{5},\ \pm3,\ \pm5,\ \pm15$

c)

$\pm\frac{1}{15}\pm\frac{1}{5}\pm\frac{1}{3}\pm1,\ \pm\frac{5}{3},\ \pm3\pm5$

d)

$\pm\frac{1}{15}\pm\frac{1}{5}\pm\frac{1}{3}\pm1,\ \pm\frac{5}{3}\pm5,\ \pm15$

4.

Find all zeros for the polynomial function given one of the factors of the function is (x+3).

$f\left(x\right)=2x^3+5x^2-6x-9$

a)

$x=-3,-1$

b)

$x=-3,\ -1,\ \frac{3}{2}$

c)

$x=1,\ 3$

d)

$x=\ \frac{-3}{2},\ 1,\ 3,\$

5.

Which statement is NOT true regarding the graphed polynomial function?

a)

The factors are $\left(x+1\right)\left(x-1\right)^2\left(x-2\right)$

b)

The factors are $\left(x-1\right)\left(x+1\right)^2\left(x+2\right)$

c)

The solutions are -1, 1, 2

d)

The intercepts are

(-1, 0), (0, 1), (1, 0), (2, 0)

6.

Solve the polynomial function. You may use a graphing utility to help you.
$f\left(x\right)=x^4+4x^3-17x^2-20x+60$

a)

$zeros:\ 2,\ -6,\ \sqrt{5},\ -\sqrt{5}$

b)

$zeros:\ -2,\ 6,\ \sqrt{5},\ -\sqrt{5}$

c)

$zeros:\ 2,\ -6,\ 5,\ -5$

d)

$zeros:\ 2,\ -6,\ \ 5i,\ -5i$

7.

State all of the intercepts for the graph of the rational function.

$f\left(x\right)=\frac{x^2+x-6}{x-5}$

a)

$\left(-3,\ 0\right),\ \left(2,\ 0\right),\ \left(0,\ \frac{6}{5}\right)$

b)

$\left(0,\ -3\right),\ \left(0,\ 2\right),\ \left(\frac{6}{5},\ 0\ \right)$

c)

$\left(0,\ -3\right),\ \left(0,\ 2\right),\ No\ y\ intercept.$

d)

$\left(-3,\ \ 0\right),\ \left(\ 2,\ 0\right),\ \ No\ y\ intercept.$

8.

State all of the the asymptotes and holes (if any) for the graph of the rational function.

$f\left(x\right)=\frac{x^2+5x-6}{x^2-1}$

a)

$x=3,\ x=2,\ y=\pm1,\ no\ hole$

b)

$x=3,\ x=2,\ y=\pm1,\ \ hole@\ x=1$

c)

$x=-1,\ \ y=1,\ \ hole@\ x=1$

d)

$x=-1,\ \ y=1,\ no\ hole$

9.

Match the picture of the graph to its corresponding rational equation below.

a)

$f(x)=\frac{x^2}{x^2+x}$

b)

$f(x)=\frac{4x^2}{x^2+x-12}$

c)

$f(x)=\frac{4x^2}{2x^2+x-12}$

d)

$f(x)=\frac{8x^2}{2x^2-x+12}$

10.

State all of the the asymptotes and holes (if any) for the corresponding graph of the rational function.

$f\left(x\right)=\frac{2x^2+x+1}{x+1}$

a)

$x=-1,\ \ y=2,\ no\ hole$

b)

$x=-1,\ y=2x,\ \ hole@\ x=0$

c)

$x=-1,\ \ y=2x-1,\ \ no\ hole$

d)

$x=-1,\ \ y=2x-1,\ \ hole@\ x=0$

11.

State the domain in interval notation for the corresponding graph of the rational function.

$f\left(x\right)=\frac{x^2+x-6}{x-5}$

a)

$Domain:\ x\ne\pm5\$

b)

$Domain:\ \left(-\infty,\ -3\right)\cup\left(5,\ +\infty\right)\ \ \ \$

c)

$Domain:\ \left(-\infty,\ -5\right)\cup\left(3,\ +\infty\right)\$

d)

$Domain:\ \left(-\infty,\ 5\right)\cup\left(5,\ +\infty\right)\$

12.

State all of the the asymptotes for the corresponding graph of the rational function.

a)

$x=5,\ y=6$

b)

$x=5,\ y=x+6$

c)

$x=5,\ y=-x+6$

d)

$x=5,\ y=\frac{1}{2}x+6$

13.

In set notation, state the domain of the simplified composite.

$f\left(x\right)=\frac{4}{x-3},\ \ \ g\left(x\right)\ =\ \frac{10}{x}$

$f\left(g\left(x\right)\right)$

a)

$\left\{x\parallel\ x\ne0,\frac{10}{3}\right\}$

b)

$\left\{x\parallel\ x\ne0,\ 3\right\}$

c)

$\left\{x\parallel x\ne0\right\}$

d)

$\left\{x\parallel\ x\ne\frac{10}{3}\right\}$

e)

$\left\{x\parallel\ x\ne3\right\}$

14.

Which of the following equations is the exponential function that contains the following two points?

$\left(-5,\ 96\right)\ \&\ \left(2,\ \frac{3}{4}\right)$

a)

$y=2\left(\frac{1}{3}\right)^x$

b)

$y=3\left(\frac{1}{2}\right)^x$

c)

$y=2\left(\frac{1}{4}\right)^x$

d)

$y=4\left(\frac{1}{2}\right)^x$

15.

Which statement below is the inverse of $f(x)=\frac{2x+1}{x-1}$

a)

$f^{-1}(x)=\frac{x}{x-\frac{1}{2}},\ x\ne\frac{1}{2}$

b)

$f^{-1}(x)=\frac{x-\frac{1}{2}}{x+1},\ x\ne-1$

c)

$f^{-1}(x)=\frac{x-1}{x-2},\ x\ne2$

d)

$f^{-1}(x)=\frac{x+1}{x-2},\ x\ne2$

16.

Solve the logarithmic equation.

$\log_5x=3$

x = __________

a)

15

b)

1

c)

25

d)

125

17.

Use the properties of logarithms to find the exact value of each expression.

$\log_82+\log_84=$

a)

1

b)

2

c)

4

d)

.86

18.

Choose the correctly condensed logarithm

$2\log_3u-\log_3z$

a)

$2\log_3\left(\frac{u}{z}\right)$

b)

$\log_3\left(\frac{u^2}{z}\right)$

c)

$\log_3\left(u^2-z\right)\ \$

d)

$2\log_3\left(u-z\right)$

19.

Choose the correct expanded common logarithm:

$\log(xy^2)$

a)

$\log x+2\log y$

b)

$\log x+\log y^2$

c)

$\log x-2\log y$

d)

$\log x+\log y+\log2$

20.

Solve for x in the logarithmic equation.

$\log_6\left(x+4\right)+\log_6\left(x+3\right)=1$

a)

-1

b)

4

c)

-3

d)

6

21.

Solve for x in the exponential equation.

$7^x=12$

Round your answer to the nearest hundreth.

a)

1.28

b)

1.39

c)

0.92

d)

1.71

22.

Solve for x in the exponential equation.

$8^{x+1}=3$

Round your answer to the nearest hundreth.

a)

-0.47

b)

-0.52

c)

-0.63

d)

-0.71

23.

Solve for the exact value of x in the exponential equation.

$2^{x-1}=3^{x+1}$

Then approximate your answer to the nearest hundreth.

a)

$x=\frac{\log\left(6\right)}{\log\left(\frac{2}{3}\right)},\ \ Therefore\ x=-4.42$

b)

$x=\frac{\log3-\log2}{\log2-\log3},\ \ Therefore\ x=-1$

c)

$x=\frac{\log6}{\left(\log2-\log3\right)},\ \ Therefore\ x=4.26$

d)

$x=\frac{2\log3}{\left(\log2-\log3\right)},\ \ Therefore\ x=-5.42$

24.

Find the amount that results from the investment.

Invested: $700

Time: 2 years

Interest rate: 6%

Compounding: daily

Type your answer WITHOUT dollar signs and commas, rounded to the nearest penny.

a)

$789.24

b)

$742.56

c)

$722.38

d)

$704.44

25.

How many years will it take for an initial investment of $25,000 to grow to $80,000 at a rate of 7% compounded continuously?

Type your answer rounded to the nearest hundredth. No label needed.

a)

16.62

b)

16.21

c)

16.87

d)

17.34

26.

Which graph corresponds to

(x+2)²+ (y-3)²=36

a)

A

b)

B

c)

C

d)

D

27.

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

a)

(x - 2)²+ (y + 5)²= 36

b)

(x - 5)² + (y + 2)² = 6

c)

(x + 5)²+ (y - 2)²= 36

d)

(x + 2)²+ (y - 5)²= 6

28.

Where is the vertex of $y=3\left(x-26\right)^2+14$ ?

a)

(26, 14)

b)

(14, 26)

c)

(-26, 14)

d)

(3, 14)

e)

(3, 26)

29.

Which transformations are involved in the equation $y=\frac{1}{2}\sqrt{x+1}-1$ ?

a)

V Stretch by 2, H shift left 1, V Shift down 1

b)

V Stretch by 2, H shift right 1, V Shift down 1

c)

V Shrink by 1/2, H shift left 1, V Shift down 1

d)

V Shrink by 1/2, H shift right 1, V Shift down 1

30.

What is the equation of the graph below?

a)

f(x ) = I x + 4 I + 2

b)

f(x ) = -I x - 4 I + 2

c)

f(x ) = I x - 4 I + 2

d)

f(x ) = -I x + 4 I + 2

31.

Describe the intervals over which the given function is decreasing.

a)

(-∞, 0) U (2, ∞)

b)

(5, -4) U (2, -3)

c)

(-3, 0) U (2, 3)

d)

(5, -4) U (0, -3)

32.

What is the domain of this function?

f(x) = √(x-2)

a)

[2,∞)

b)

(-∞,2]

c)

(-2, ∞)

d)

(-∞,2) U (2, ∞)

33.

What is f(3)?

a)

3

b)

14

c)

6

d)

√6

34.

What is the value of f(0)?

a)

-2

b)

2

c)

4

d)

-2 and 2

35.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

36.

Use the graph to find the values of x where $f\left(x\right)\ge g\left(x\right)$ in interval notation.

a)

$\left[-1,3\right]$

b)

$\left(-1,3\right)$

c)

$\left(-\infty,-1\right)U\left(3,\infty\right)$

d)

$\left(-\infty,-1\right]U\left[3,\infty\right)$

37.

The price p (in dollars) and the quantity x items of a certain product sold follow the demand equation $p=-\frac{1}{3}x+400$ . Express the revenue R as a function of x. (Remember R=xp). Find the revenue after 447 units are sold.

a)

$R\left(x\right)=-\frac{1}{3}x^2+400x,\ \ \$ Revenue of 447 units; $112,197

b)

$R\left(x\right)=-\frac{1}{3}x^2+400x,\ \ \$ Revenue of 447 units; $251

c)

$R\left(x\right)=-\frac{1}{3}x^2+400x,\ \ \$ Revenue of 447 units; $120,000

d)

$R\left(x\right)=-3p^2+400p,\ \ \$ Revenue of 447 units; $115,340

Pre Calculus S2 Final Exam

Total questions: 37

Worksheet time: 1hrs 25mins

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