Free Printable A2 Gen Final Review

1.

To which intervals could we restrict the domain of f(x) to make it an invertible function? Choose all answers that apply.

a)

-6 ≤ x ≤ -2

b)

-4 ≤ x ≤ 4

c)

-2 ≤ x ≤ 2

d)

none of the above

2.

Find the inverse function

a)

A) f(x) = 1/x

b)

B) f(x) = x^2

c)

C) f(x) = x + 1

d)

D) f(x) = e^x

3.

Find the inverse function

a)

A) x + 1

b)

B) x - 1

c)

C) 1/x

d)

D) x^2

4.

$g\left(g\left(-5\right)\right)$

a)

1

b)

-0.25

c)

3

d)

-1

5.

a)

9 - 8/3

b)

9 + 8/3

c)

3

d)

1/3

6.

Decompose the following composite function: $f\left(g\left(x\right)\right)=h\left(x\right)=\left(x^2-10\right)+3$

a)

$f\left(x\right)=x^2-10$

b)

$f\left(x\right)=x+3$

c)

$g\left(x\right)=x^2-10$

d)

$g\left(x\right)=x+3$

7.

Decompose the following composite function: $f\left(g\left(x\right)\right)=h\left(x\right)=\frac{1}{x+2}$

a)

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

b)

$f\left(x\right)=x+2$

c)

$g\left(x\right)=x+2$

d)

$g\left(x\right)=\frac{1}{x}$

8.

Evaluate the following logarithm:

log₃(¹/₃)

a)

-2

b)

-¹/₂

c)

-1

d)

¹/₂

9.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

10.

$Evaluate\ \log_61$

(a)

11.

Choose the correct expanded common logarithm:

$\log(3x)^2$

a)

$2\log(3+x)$

b)

$2\log3+\log x$

c)

$\log3+2\log x$

d)

$2(\log3+\log x)$

12.

If $\log_BA=\frac{\log A}{\log B}$ , then $\log_{12}245=$

a)

$\log\frac{245}{12}$

b)

$\log\frac{12}{245}$

c)

None of these

13.

a)

x = 5 and x = -2

b)

x = -2

c)

x = 5

d)

x = -10 and x = 10

14.

Solve $\log7+\log\left(x^2-4\right)=\log35$

a)

$x=3$

b)

$x=-2$

c)

$x=4$

d)

$x=-3$

15.

Describe the transformation from dotted to solid.

a)

f(x + 5) + 3

b)

f(x +3) + 5

c)

f(x - 5) + 3

d)

f(x - 3) + 5

16.

The graph of f(x) is represented below...

Which graph represents f(-x)?

a)

b)

c)

d)

17.

State the domain and range using "inequality" notation.

a)

x ≥ -4 and y ≥ 2

b)

x ≥ 4 and y ≥ 2

c)

x > -4 and y > 2

d)

D: [-4, ∞) and R: [2, ∞)

18.

Simplify:

$\left(8-7i\right)^2$

a)

64 - 49i

b)

16 - 14i

c)

15 - 112i

d)

64 + 49i

19.

Which of the following represents the graph below?

a)

b)

c)

d)

20.

Which is the graph of the rational equation:

a)

b)

c)

d)

21.

Choose all of the functions that have a hole:

a)

$f\left(x\right)=\frac{x^2+7x}{x^2-6x-7}$

b)

$f\left(x\right)=\frac{\left(x+8\right)\left(x-2\right)}{\left(x+2\right)\left(x+8\right)}$

c)

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

d)

$f\left(x\right)=\frac{x^2-9}{2x-6}$

e)

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

22.

Find the vertical asymptote(s).

a)

x = 3 and x = -7

b)

x = 3

c)

x = -7

d)

x = -4

23.

Which of the following is the equation of a rational function with a hole at $x = 1$ ?

a)

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

b)

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

c)

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

d)

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

24.

Write the equation of a rational function with vertical asymptotes at $x = -3$ and $x = 2$ , and a horizontal asymptote at $y = 0$ .

a)

$f(x) = \frac{1}{(x + 3)(x - 2)}$

b)

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

c)

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

d)

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

25.

What is the horizontal asymptote of f(x)?

$f\left(x\right)=\frac{x^2-25}{x+5}$

a)

y = 0

b)

y = x

c)

x = 0

d)

There is no horizontal asymptote.

26.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

27.

What is the equation of the graph?

a)

b)

c)

d)

28.

Write an equation for a rational function with an x-intercept of (–1, 0), a hole at x = 3, and a VA at x = 4.

a)

y= (x-1)(x+3) / (x+4)(x+3)

b)

y= (x-4)(x-3) / (x+1)(x-3)

c)

y= (x+1)(x-3) / (x-4)(x-3)

d)

y= (x+4)(x+3) / (x+1)(x+3)

29.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

30.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

31.

Where is the graph increasing?

a)

(-∞, -2.55) U (2.55, ∞)

b)

(0, ∞)

c)

(-2.55, 0) U (2.55, ∞)

d)

(-6.25, 36)

32.

Pick the statements that does apply to this polynomial.

a)

It is an odd degree function.

b)

It is an even degree function.

c)

It has a negative leading coefficient.

d)

It has 3 real roots.

e)

It has an absolute maximum

33.

Find all rational zeros, one zero has been given.
f(x) = x³-3x²-x+3; 3

a)

2,4,3

b)

-1,1,3

c)

3,2,1

d)

4,5,6

34.

Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)

a)

x = 5, (2/3), 6, (7/4)

b)

x= -5, (3/2), (-4/7), 6

c)

x= 5, (-3/2), (4/7), -6

d)

x= 6, 5, -2/3, -4/7

35.

What are the zeros for this function?

a)

b)

c)

d)

36.

Solve for all zeros:

x\left(x-1\right)\left(x+2\right)\left(3x-5\right)\left(x^2+1\right)\ =\ 0

a)

$x=-1,\ 2,\ -\frac{5}{3},\ \pm i$

b)

$x=0,\ -1,\ 2,\ -\frac{5}{3},\ \pm i$

c)

$x=0,\ 1,\ -2,\ \frac{5}{3},\ \pm i$

d)

No solution

37.

Factor: $2x^2+7x\ +6$

a)

$\left(2x+3\right)\left(x+2\right)$

b)

$\left(x+4\right)\left(x+3\right)$

c)

$\left(x+2\right)\left(x+6\right)$

d)

$\left(x+1\right)\left(x+6\right)$

38.

Solve:

2x^3+5x^2=7x

a)

$x=\ -\frac{7}{2}\ and\ x=\ 1$

b)

$x\ =\ -2,\ x\ =\ 0,\ \&\ x=\ 7$

c)

$x=-2,\ x\ =\ 0,\ \&\ x\ =\ \frac{7}{2}$

d)

$x=\ -\frac{7}{2},\ x=\ 0,\ \&\ x\ =\ 1$

39.

Identify the domain and range of each. Then sketch the graph.

a)

b)

c)

d)

40.

Find the zeros: y = x(x - 1)(x + 3)

a)

0, 1, -3

b)

-3, 1

c)

-1, 3, 0

d)

-1, 3

41.

What is the relative max of this function?

a)

x = 5

b)

infinity

c)

there is no relative maximum

d)

2.5 and it occurs at x = 5

42.

What is the Range of the function being graphed?

a)

(-∞, ∞)

b)

(7, ∞)

c)

(-∞, 7)

d)

(-1, 1)

43.

Check all the intervals where this graph is increasing.

a)

(-∞, -1)

b)

(-1, 0)

c)

(0, 1)

d)

(1, ∞)

44.

What is the equation of the Vertical Asymptote of $y=\frac{3}{x-4}+2$

a)

$x=2$

b)

$y=2$

c)

$x=4$

d)

$y=4$

e)

No Vertical Asymptote

45.

Rewrite as a single logarithm:

\log_260\ -\ \log_210

a)

$\log_26$

b)

$\log_250$

c)

$\frac{\log_260}{\log_210}$

d)

$\log_270$

46.

Solve for x: $\log\left(x+9\right)+\log x=\log22$

a)

2, -11

b)

2

c)

-11

d)

11

47.

a)

-10

b)

5

c)

-6

d)

10

48.

a)

i

b)

ii

c)

iii

d)

iv

49.

Which is the inverse for the function

a)

a.

b)

b.

c)

c.

d)

d.

50.

Solve. Check for extraneous solutions.

ln(x+1)-ln(2)=5

a)

x=(e⁵-1)/2

b)

No Solution

c)

x=2e⁵-1

d)

x=2e⁵+1

A2 Gen Final Review

Total questions: 50

Worksheet time: 3hrs 32mins

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