PreCalculus Semester 1 Final Exam Study Guide

PreCalculus

Sem. 1 Final Exam Study Guide

Exam 1 Topics: Function Basics

• Slope

• Equations of Lines

• Functions

• Interval Notation & Domain and Range

• Piecewise Functions

• Composite Functions

• Inverse Functions

Multiple Choice

Write an equation of a line that passes through the point (5,-1) and is parallel to the line y = (-3/5)x -3

• y = (-3/5)x + 2

• y = (-3/5)x -2

• y = (3/5)x + 2

• y = (5/3) + 2

Multiple Choice

Write an equation of the line in point slope form containing (-1,1) and (4,-9).

• y +1 = - 2(x - 1)

• y = -2x - 1

• y - 1 = - 2(x + 1)

• 2x + y = -1

Multiple Choice

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

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

Multiple Choice

What is f when x equals 4?

• -5
• 0
• 3
• 6

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

• 19
• 23
• -10
• None of these.

Multiple Choice

Given f(x) = 2x and g(x) = x² + 3

find f(g(x)).

• x² + 2x + 3

• 4x² + 3

• 2x² + 3

• 2x² + 6

Multiple Choice

p(x) = 3x + 4
q(x) = 2x²
Find q(p(-2))

• 8
• -8
• 28
• None of these.

Multiple Choice

What is the slope of the line that passes through (1, -19) and (-2, -7)?

• -4

• $\frac{26}{3}$

• $-\frac{1}{4}$

• $\frac{1}{26}$
  

Multiple Choice

What is the RANGE of the function?

• (-∞, +∞)
• (-∞, 4]
• (-∞, 4)
• [0, 4]

Multiple Choice

Write the equation of the line in standard form through the points (-6, -19) and (2, 5).

• -3x - y = -1

• -3x + y = 1

• 3x - y = 1

• y = 3x - 1

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

• D: {1, -3, -4,}
  R: {0, 1, 2, -4}
• D:{0, 1, 2, -4}
  R:{1, -3, -4}
• D:{0, 1, 2, 3, 4}
  R:{1, -3, -4}

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Exam 2 Topics: Graphing Characteristics

• Even or Odd Functions

• Intervals of Increase/Decrease

• Maximums & Minimums

• Parent Functions

• Transformations

Multiple Choice

Is the function even, odd, or neither?

f(x) = x² + 2

• Even

• Odd

• Neither

Multiple Choice

Is the table even, odd or neither?

• Even

• Odd

• Neither

Multiple Choice

The function in the graph is:

• even
• odd
• neither even nor odd
• both even and odd

Multiple Choice

The function shown in the graph is:

• even
• odd
• neither even nor odd
• both even and odd

Multiple Choice

g(x)=f(x-4)
Describe the transformation to f(x) that results in g(x).

• f(x) has been translated to the right 4.
• f(x) has been translated to the left 4.

Multiple Choice

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Multiple Choice

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

• $\left(-7,\ -6\right)\ and\ \left(-2,\ 4\right)$

• $\left(-7,\ 0\right)\ and\ \left(-2,\ 4\right)$

• $\left(-7,\ -6\right)\ and\ \left(-2,\ 0\right)$

• $\left(-7,\ 0\right)\ and\ \left(4,\ 5\right)$

Multiple Choice

What is/are the increasing interval(s) for the function shown?

• $\left(-3,\ 1\right)$

• $\left(4,\ 8\right)$

• $\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$

Multiple Choice

What is the maximum value (y-value only)?

• 5

• 0

• -5

• 2

Multiple Choice

What is the minimum value (y-values only)?

• 0

• -5

• -3

• -1

Exam 3 Topics: Polynomials

• Polynomials

• Classify Polynomials

• GCF

• Trinomials

• Difference of Squares

• Sum & Difference of Cubes

• Grouping

Multiple Choice

Factor Completely:

256x⁴ - 81

• (16x² + 9)(16x² - 9)

• (16x² + 9)(4x + 3)(4x - 3)

• (4x² + 9)(4x² - 9)

• (16x² + 9)(2x + 6)(2x -6)

Multiple Choice

Factor: 27x³ + 8

• (3x + 2)(9x² - 6x + 4)

• (9x + 2)(3x² + 18x + 4)

• (3x²+4)(9x + 2)

• (27x + 8)(x² - 216x + 64)

Multiple Choice

Fully Factor the Following

25x²-81

• (5x-9)²

• (5x+9)(5x-9)

• 25(x-9)²

• (9x+5)(9x-5)

Multiple Choice

Factor p³ - 3p² - 16p + 48

• p² ( p - 3) (p - 3)

• (p² - 16) (p - 3)

• (p + 4) (p - 4) (p - 3)

Multiple Choice

Which binomials are a difference of two squares?

I. 6a²-25

II. 4x²+16

III. b²-9

IV. 49y²-64

• I only

• III only

• III and IV

• II, III, and IV

Multiple Choice

Which expression below represents a polynomial?

• $2x^{-3}+x^2-10$

• $\frac{1}{x}-5$

• $x^{0.5}+6x-3$

• $x^2-3x+7$

Multiple Choice

Factor out the GCF:

9x⁴y - 24x²

• 9x²y(x² - 3)

• 3x³(3xy - 8)

• 3x²(3x²y - 8)

• x²(9x²y - 24)

Multiple Choice

Factor:

3x² + 5x - 12

• (3x + 4)(x-3)

• (3x - 4)(x + 3)

• (3x + 3)(x -4)

• (3x - 3)(x + 4)

Multiple Choice

Factor

x² - 9x + 18

• A. (x - 6)(x - 3)

• B. (x + 6)(x - 3)

• C. (x - 9)(x - 2)

• D. (x - 6)(x + 3)

Multiple Choice

Factor completely:

3x² + 18x +15

• 3(x² + 6x + 5)

• (x + 5)(x + 1)

• 3(x + 5)(x + 1)

• Prime

Multiple Choice

What is the degree of the polynomial:

7x³ – 8x² + 9

• 5

• 2

• 6

• 3

Multiple Choice

What is the degree of the polynomial:

7x³ – 8x² + 9

• 5

• 2

• 6

• 3

Exam 4 Topics: Polynomial Division

• Polynomial Long Division

• Synthetic Division

• Remainder Theorem

• Factor Theorem

• Rational Root Theorem

Multiple Choice

4x⁴+4x³-9x²-x+2 ÷ x-1

• 4x³+8x²-7x-2
• 4x³+19x²-x-2
• 4x³+8x²-x-9
• 4x³+8x²-x-2

Multiple Choice

• 2x - 5
• x - 4 + (3/4x - 5)
• 2x + 4 + (3/4x - 5)
• 2x + 4

Multiple Choice

x⁴ - 10x³ + 35x² - 50x + 24 ÷ x² - 3x + 2

• x² - 7x + 12

• x³ + 3x² + 4x - 1

• x² - 1

• x² + 7x - 12

Multiple Choice

Use synthetic division or long division.

 $\frac{x^3-x^2+4}{x+2}$  

•  $x^2+3x+6+\frac{-8}{x+2}$  

•  $x^2-3x+6+\frac{-8}{x+2}$  

•  $x^2-2x+6+\frac{6}{x+2}$  

•  $x^2-3x+6+\frac{6}{x+2}$  

Multiple Choice

Use long division to divide.

 $\frac{x^4+7x^3+17x^2+20x}{x^2+4}$  

•  $x^2+13x+7+\frac{-52}{x^2+4}$  

•  $x^2+7x+\frac{13x-8}{x^2+4}$  

•  $x^2+7x+13+\frac{-8x-52}{x^2+4}$  

•  $x^2+1+\frac{1}{x^2+4}$  

Multiple Choice

What is the remainder when x³ - 4 is divided by x+2?

• -2

• -6

• -12

• 0

Multiple Choice

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.

• No, (x-2) is not a factor. The remainder is zero.

• Yes, (x-2) is a factor. The remainder is zero.

• No, (x-2) is not a factor. There is a remainder.

Multiple Choice

List all the possible rational zeros 
h(x) = x³ - 5x²+2x+12

• 1,2,3,4,6,12
• 1,2,6,12
• 1,2,3,4,6,12,-1,-2,-3,-4,-6,-12

Multiple Choice

List all possible rational zeros
f(x) = 3x⁵-5x²+x+6

• 1, 2, 3, 6, -1, -2, -3, -6
• 1/3,2/3,1,2,3,6,-1/3,-2/3,-1,-2,-3,-6
• 1/3,2/3,1,2,3,6

Multiple Choice

Factor completely using Rational Root Theorem:

2x³ - 11x² + 12x + 9 = 0

• (x+1)(x-1)(x-3)

• (x+1)(2x-3)(x-3)

• (2x+1)(x-3)(x-3)

• (2x+1)(x-1)(x-3)