Function Descriptors
Scatterplots/Transformations
Absolute Value Equations/Inequalities
Quadratics/Complex Numbers
Polynomials/Rational Expressions
100
What is the domain and range of this function? Give your answer in interval notation.
domain: (-∞,∞)
range: [0,∞)
100
Describe the relationship between number of games and score.
As the number of games increases, the score increases.
100
Solve 3 + |2x| = 7
x = 2, -2
100
Solve x2 + 6x + 8 = 0.
x = -2 and x = -4
100
Find the difference:
5x2 - 4x + 3 - (2x2 - 7x + 8)
3x2 +3x -5
200
What are the x-intercepts (zeros) and y-intercepts of this function?
X-intercepts (zeros): x = -2 (x = 2 is NOT because there is a hole)
Y-intercepts: y = 4
200
State the parent function and describe the transformation(s).
y = x + 5
parent function: linear
transformations: shift up 5 units
200
Solve the following absolute value inequality:
2|x| ≤ 8
-4 ≤ x ≤ 4
200
Complete the following operation:
5i + 3 - (4i - 6)
i + 9
200
Find the product:
(5x - 4)(3x2 - x + 2)
15x3 - 17x2 +14x - 8
300
For which intervals is this function increasing and decreasing?
Increasing: (-4,0)
Decreasing: (0,4)
300
State the parent function and describe the transformation(s).
y = 3x2 - 7
parent function: quadratic
transformations(s): vertical stretch by a factor of 3, shift down 7 units
300
Solve 3 - |5x| = 8
No solution, absolute value can't be negative
300
Find the solutions of the following system of equations:
x + y = 5
y = x2 − 25
(5,0) and (-6,11)
300
Simplify the following rational expression:
(x-1)/(x-5)
400
At which point on this graph does the absolute maximum occur?
(0,4)
400
Determine the equation for the line of best fit for this data and use it to estimate the number of gallons bought when someone spends $6.
Equation for the line of best fit: y = 0.198x + 0.575
gallons: 1.76
400
Ms. Cislo sets her coffee maker to brew coffee so it is ready when she wakes up in the morning. The proper brewing temperature for coffee tea is 210º F plus or minus 5 degrees. Write and solve an absolute value equation representing the maximum and minimum brewing temperatures for coffee.
Equation: |x – 210| = 5
Case 1: x – 210 = 5, so x = 215
Case 2: x – 210 = -5, so x = 205
Solutions:
x = 205 (minimum temperature)
x = 215 (maximum temperature)
400
Solve -2d2 + 3d - 5 = 0
x = (-3 ± i√31)/-4
400
Find the quotient:
2(x+6)/(3x-2)
500
What is the end behavior of this function?
As x → ∞, f(x) → 4
As x → -∞, f(x) → ∞
500
If the equation y = √(x + 1) - 3 is translated right 3 units, up 1 unit, reflected across the y-axis, and stretched vertically by a factor of 2, what is the resulting equation?
y = 2√(-x - 2) - 2
500
At the Brooks Company, the average starting salary for a new employee is $37,600, but the actual salary could differ from the average by as much $2590. Write an absolute value inequality to describe this situation and solve the inequality to find the range of the starting salaries.
Inequality: |x – 37600| ≤ 2590
Case 1: x – 37600 ≤ 25900, so x ≤ 40190
Case 2: x – 37600 ≥ −25900, so x ≥ 35010
Solution: $35,010 ≤ x ≤ $40,190
500
Solve the following quadratic inequality:
x2 - 6x - 9 < 7
-2 < x < 8
500
(-3x+2)/[(x+2)(x-1)(x-2)]