Free Printable 112 Final Exam Review

1.

Look at the picture. Select the correct interval notation for the given number line.

a)

(-∞, -8) U (-4, ∞)

b)

(-∞, -8] U [-4, ∞)

c)

(-8, -4)

d)

[-8, -4]

2.

a)

Function

b)

Not a Function

3.

The domain of a rational function is...

a)

the $x-$ values that make the denominator equal 0

b)

the range of possible $y-$ values the function reaches

c)

the range of acceptable $x-$ values that may be plugged into the function

d)

the $y-$ intercept

4.

Find the domain of

f\left(x\right)\ =\ \frac{x-3}{x+4}

.

a)

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

b)

$\left(-\infty,3\right)\cup\left(3,\infty\right)$

c)

$\left(-\infty,-4\right)\cup\left(-4,\infty\right)$

d)

$\left(-\infty,-4\right)\cup\left(-4,3\right)\cup\left(3,\infty\right)$

5.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

6.

Consider the following function.
$f\left(x\right)\ =\ x^2+4x+3$
Find the vertex.

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

7.

Determine the implied domain of the following function. Express your answer in interval notation.
$f\left(x\right)\ =\ \sqrt{x+4}+1$

a)

$\left(4,\ \infty\right)$

b)

$\left(-4,\ \infty\right)$

c)

$\left[-4,\ \infty\right)$

d)

$\left(-\infty,\ -4\right]$

8.

Consider the following function.
$r\left(x\right)=\left(x-5\right)^2-1$
Find the vertex.

a)

$\left(-1,\ -5\right)$

b)

$\left(-5,1\right)$

c)

$\left(-5,-1\right)$

d)

$\left(5,-1\right)$

9.

Consider the following function.
$r\left(x\right)\ =\ -x^2+6x-8$
Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s).

a)

$\left(-2,0\right)\ and\ \left(4,0\right)$

b)

$\left(2,0\right)\ and\ \left(4,0\right)$

c)

$\left(2,0\right)\ and\ \left(-4,0\right)$

d)

$\left(-2,0\right)\ and\ \left(-4,0\right)$

10.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

11.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

12.

Solve $x^2\ -\ 5x\ +\ 10\ =\ 0$

a)

$\frac{5-i\sqrt{15}}{2},\ \frac{5+i\sqrt{15}}{2}$

b)

$\frac{5-\sqrt{15}}{2},\ \frac{5+\sqrt{15}}{2}$

c)

$\frac{5-i\sqrt{65}}{2},\ \frac{5+i\sqrt{65}}{2}$

d)

$\frac{5-\sqrt{65}}{2},\ \frac{5+\sqrt{65}}{2}$

13.

What are the transformations?
y=(x-2)³+4

a)

Horz shift right 2 Vert shift up 4

b)

Horz shift left 2 Vert shift up 4

c)

Horz shift right 2 Vert shift down 4

d)

Horz shift left 2 Vert shift up 4

14.

What is the range of the graph?

a)

[1, ∞)

b)

(1, ∞)

c)

(-∞, ∞)

d)

none of these

15.

What is the domain of this function?

a)

Domain: (-∞, ∞)

b)

Domain: (-1, ∞)

c)

Domain: [-1, ∞)

d)

none of the above

16.

Simplify the following quotient:
(x³ − 6x + 9) ÷ (x + 3)

a)

x² + 3x + 3 + 18/(x + 3)

b)

x² − 9x + 36

c)

x² − 3x + 3

d)

x² + 3x + 3

17.

Use synthetic division to evaluate the function at f(2).
f(x) = 6 + 2x² − 3x³

a)

Bottom row of synthetic division: −3, −4, −8, −10
f(2) = −10

b)

Bottom row of synthetic division: −3, 8, −16, 38
f(2) = 38

c)

Bottom row of synthetic division: −3, 4, 8, −10
f(2) = −10

d)

Bottom row of synthetic division: −3, 8, 16, 38
f(2) = 38

18.

Determine if this equation can represent y as a function of x.
x² + y² = 25

a)

Yes.

b)

No.

c)

Sometimes, but not always.

d)

Circles have an infinite number of sides, so they are a little too circular for me. I only trust squares.

19.

Determine (f − g)(x).
f(x) = x + 2
g(x) = x − 3

a)

5

b)

2x + 5

c)

x − 1

d)

x² − x − 6

20.

Find the slope between (4, -8) and (-1, 3).

a)

-5/11

b)

11/5

c)

5/11

d)

-11/5

21.

f(x)=x²-2x+1
Evaluate the function for f(-1).

a)

f(-1)=4

b)

f(-1)=0

c)

f(-1)=2

d)

f(-1)=-1

22.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

23.

Solve:
_{log (−2a + 9) = log (7 − 4a)}

a)

-5

b)

-1

c)

1

d)

5

24.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

25.

E = mc² solve for m

a)

m = sqrt(E/c)

b)

m = sqrt(E)/c

c)

m = E/c²

d)

m = money

26.

Simplify √20

a)

2√5

b)

4√5

c)

5√2

d)

3√6

27.

Which function represents the graph of f(x) = | x | translated 3 units to the right?

a)

g(x) = | x - 3 |

b)

g(x) = | x + 3 |

c)

g(x) = |x| - 3

d)

g(x) = |x| + 3

28.

Which function represents the graph of f(x) = x² translated 5 units down?

a)

f(x) = x² + 5

b)

f(x) = x² - 5

c)

f(x) = (x-5)²

d)

f(x) = (x + 5)²

29.

.
If the blue is f(x)=x^2,then the red must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

30.

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

a)

x=-4, x=3, x=-2

b)

x=-4, x=3, x=2

c)

x=-4, x=3, x=2

d)

x=4, x=3, x=2

31.

parallel to y + 2x = 4, through (2, 2); slope-intercept form

a)

y = - 2x - 6

b)

y = 2x - 6

c)

y = - 2x + 6

d)

y = - 1/2x - 3

32.

Write the equation of a line parallel to -3x + 8y = -30, through (2, -4); slope-intercept form.

(a)

33.

Solve the equation 3x + 7 = 0

a)

x = $-\frac{7}{3}$

b)

x = $\frac{7}{3}$

c)

The solution set is $\left(-\infty,\infty\right)$

d)

There is no solution

34.

Solve.

x^2\ +6x\ +9\ =\ 14

a)

$3\pm\sqrt{14}$

b)

$-3\pm\sqrt{14}$

c)

$11$

d)

$\pm\sqrt{14}$

35.

Find the equation for the circle with center (3,1) and passing through (- 1,4)

a)

$\left(x+1\right)^2+\left(y\ -\ 4\right)^2\ =\ 25$

b)

$\left(x+1\right)^2+\left(y\ -\ 4\right)^2\ =\ 5$

c)

$\left(x-3\right)^2+\left(y\ -\ 1\right)^2\ =\ 25$

d)

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

36.

Find an equation for the circle. Center at $\left(2,-8\right)$ , radius of length $\frac{1}{2}$

a)

$\left(x\ -\ 2\right)^2\ +\ \left(y\ -8\right)^2\ =\ \frac{1}{2}$

b)

$\left(x\ -\ 2\right)^2\ +\ \left(y\ +8\right)^2\ =\ \frac{1}{2}$

c)

$\left(x\ -\ 2\right)^2\ +\ \left(y+\ 8\right)^2\ =\ \frac{1}{4}$

d)

$\left(x\ +\ 2\right)^2\ +\ \left(y-\ 8\right)^2\ =\ \frac{1}{4}$

37.

Solve the following inequality and write interval notation for the solution set.
$\left|x\ +8\right|\ <\ 4$

a)

$\left(-\infty,12\right)$

b)

$\left(-\infty,-4\right)$

c)

$\left(-12,-4\right)$

d)

$\left(-\infty,-12\right)U\left(-4,\infty\right)$

38.

Solve.
$2^{3x-7}=32$

a)

$x\ =\ -2$

b)

$x\ =\ 3$

c)

$x\ =\ 4$

d)

$x\ =\ 13$

39.

$\left(-4,-4\right)\ and\ \left(5,7\right)$ Find the midpoint of the segment having the given endpoints.

a)

$\left(-9,-11\right)$

b)

$\left(-\frac{9}{2},-\frac{11}{2}\right)$

c)

$\left(\frac{1}{2},\ \frac{3}{2}\right)$

d)

$\left(1,3\right)$

40.

Express as a single logarithm and , if possible, simplify.

$3\log_ax\ -\ \log_ay$

a)

$\log_a\ \frac{x^3}{y}$

b)

$\log_a\ \frac{3x}{y}$

c)

$3\log_ax\ \div\ \log_ay$

d)

$\log_a\left(x^3-y\right)$

41.

Convert to a logarithmic equation.

$8^2\ =\ 64$

a)

$64\ =\ \log_28$

b)

$2\ =\ \log_{64}8$

c)

$64\ =\ \log_82$

d)

$2\ =\ \log_864$

42.

What is g(-2) if:

a)

-7

b)

7

c)

1

d)

-1

43.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

c)

both

d)

neither

44.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

45.

Is this an even, odd, or neither function? $f\left(x\right)=7x^8-9x^2+33$

a)

Even Function

b)

Odd Function

c)

Neither

d)

Not a function

46.

All odd functions have symmetry with respect to the origin.

a)

True

b)

False

47.

How do you find the y-intercept?

a)

replace all x-values with 0

b)

replace all y-values with 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

48.

How would you rewrite the equation after multiplying the LCD?

a)

2x-20=3x+12

b)

2x-5=3x+3

c)

4x-20=6x+12

d)

2x-20=4x+12

49.

Solve. Select BOTH solutions.
$\left|-4+x\right|=10$

a)

$6$

b)

$14$

c)

$\frac{5}{2}$

d)

$-6$

50.

To complete the perfect square trinomial in the expression x²-22x+_____, we need to add

a)

11

b)

44

c)

121

d)

144

51.

What are the values of a, b, and c in the quadratic equation 3x² - 10 = -4x

a)

a = 3x² b = -10 c = -4x

b)

a = 3 b = -10 c = -4

c)

a = 3 b = -4 c = -10

d)

a = 3 b = 4 c = -10

52.

When do you "flip the inequality symbol"?

a)

When you add or subtract a negative

b)

You always flip

c)

When you multiply or divide a negative

d)

When it's a 2-step problem

53.

Write an inequality for Graph 3.

a)

5 < x ≤ -2

b)

x ≤ -2 OR x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x < 5

54.

Match the graph to the function

a)

f(x)= -x²+3x+2

b)

f(x) = -x³+2

c)

f(x) = x³+2

d)

f(x) = ⅓x⁴-5x²+2

55.

If (x + 3) divides a polynomial function evenly, then which of these is known to be a zero of the polynomial?

a)

x = -3

b)

x = 3

c)

x = 0

d)

cannot be determined

56.

When setting up this synthetic division to divide 2x⁴ + 3x² - x + 2 by (x - 1), what number goes into the red circle?

a)

-1

b)

1

c)

2

d)

cannot be determined

57.

A polynomial factors as
f(x) = x³(x + 1)²(x - 4). List the zeros of f(x) and their multiplicity.

a)

0 multiplicity 3, 1 multiplicity 2, -4 multiplicity 1

b)

0 multiplicity 3, -1 multiplicity 2, 4 multiplicity 1

c)

1 multiplicity 2, -4 multiplicity 1

d)

-1 multiplicity 2, 4 multiplicity 1

58.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

59.

What creates a hole in the graph of a rational function?

a)

Crossing the x-axis

b)

An absence of dirt.

c)

Crossing a vertical asymptote.

d)

A factor that cancels out.

60.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

112 Final Exam Review

Total questions: 60

Worksheet time: 3hrs 37mins

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