Free Printable 1st Semester Final Review: Units 1, 2

1.

What is the domain of a relation?

a)

the set of all x-values

b)

the set of all y-values

2.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

3.

What is the DOMAIN of the graph shown?

a)

(-4, 2]

b)

[-4, 2)

c)

[2, 5)

d)

(2, 5]

4.

What is the RANGE of the following graph?

a)

[0, ∞)

b)

[0, 3]

c)

(-∞, ∞)

5.

$Given\ h\left(x\right)=3x^2-2x+8\ what\ is\ h\left(-1\right)?$

a)

13

b)

8

c)

16

d)

answer not here

6.

Find f(4)

a)

1

b)

2

c)

3

d)

4

7.

What are the extrema of the graph?

a)

Max = (2, -3), (1, 2)

Min = (-3, -1), (-1, 4)

b)

Max = (-3, -1), (-1, 4)

Min = (2, -3), (1, 2)

c)

Max = (-1, -3), (4, -1)

Min = (-3, 2), (2, 1)

d)

Max = (-3, 2), (2, 1)

Min = (-1, -3), (4, -1)

8.

Find the relative maximum and minimum

a)

Rel. max at x = -3

Rel. min at x = -3

b)

Rel. max at x = 1

Rel. min at x = -3

c)

Rel. max at x = -3

Rel. min at x = 1

d)

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

9.

What is the location of the absolute maximum for the graphed function?

a)

x = 1

b)

x = 3

c)

x = 4

d)

x = 5

e)

Does Not Exist

10.

What is the increasing interval for the function below?

a)

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

b)

$\left(-\infty,2\right]$

c)

$\left(-\infty,6\right]$

d)

$\left(-6,6\right)$

11.

What is the decreasing interval on the function shown?

a)

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

b)

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

c)

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

d)

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

12.

What is the increasing interval(s) on the function shown?

a)

$\left(-\infty,\ -15\right)\ and\ \left(9,\ -15\right)$

b)

$\left(-2,\ 9\right)\ and\ \left(2,\ \infty\right)$

c)

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

d)

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

13.

What is the y-intercept?

a)

(0, 5)

b)

(5, 0)

c)

(0, -5)

d)

(-5,0)

14.

What are the x-intercepts/zeros/roots of the graph?

a)

(-1,0)

b)

(3,0)

c)

(-1,0) and (3,0)

d)

(0,-1) and (0,3)

15.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

16.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

17.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

18.

In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

19.

The slope between the points (3, 5) and (8, 4) is _______.

a)

$-\frac{1}{5}$

b)

$\frac{1}{5}$

c)

$5$

d)

$-5$

20.

What is the average rate of change from x=0 to x=1

a)

-3

b)

3

c)

0

d)

2

21.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

22.

Which equation describes the transformation of shifting f(x)=x² two units right?

a)

x² + 2

b)

x² - 2

c)

(x + 2)²

d)

(x - 2)²

23.

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

a)

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

b)

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

c)

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

d)

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

24.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

25.

Evaluate the function when x = 4

a)

f(4) = 2(4) - 5 = 3

b)

f(4) = 2(4) - 5 = -1

c)

f(4) = ½(4) + 1 = 3

d)

f(4) = 4

26.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

27.

(f + g) (x)

a)

5x² + 3x

b)

4x² + 3x

c)

5x² - 3x

d)

4x² - 40x

28.

(f - g)(x)

a)

5x² + 3x

b)

-3x² - 13x

c)

3x² + 3x

d)

-3x² + 3x

29.

$f\left(x\right)=4x+1\ and\ g\left(x\right)=4x-3.\ Find\ f\left(x\right)\cdot g\left(x\right)$

a)

$16x^2+8x-3$

b)

$16x^2-8x+3$

c)

$16x^2-8x-3$

d)

$16x^2-16x-3$

30.

When f(x) = 2x and g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

31.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

32.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

33.

a)

Inverse Functions

b)

Not Inverse Functions

34.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

35.

What is the degree of the polynomial?

3y² + y⁴ + 4

a)

2

b)

3

c)

4

d)

5

36.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

37.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

38.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and
x→ ∞, y→⁻∞

b)

x → ∞, y→ ∞ and
x→⁻∞, y→∞

c)

None of these

d)

x →∞,y→⁻∞ and
x→∞, y→⁻∞

39.

Solve for m by factoring.

a)

A

b)

B

c)

C

d)

D

40.

Solve for x by factoring.

a)

A

b)

B

c)

C

d)

D

41.

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

42.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

43.

If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

44.

Which root has even multiplicity?

a)

1

b)

-4

c)

-1

d)

2

45.

Solve using long division $\left(2x^2+6x-20\right)\div\left(2x-4\right)$

a)

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

b)

$x-8$

c)

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

d)

$x+5$

46.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

47.

$\frac{x^2+12x+27}{x+9}$ Divide using synthetic division.

a)

x+3

b)

x+9

c)

x-3

d)

x-9

48.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

49.

What is the remainder of (x³ - 5x² - 8x +1) ÷ (x + 1)?

a)

-13

b)

1

c)

3

1st Semester Final Review: Units 1, 2

Total questions: 49

Worksheet time: 1hrs 14mins

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