Solving Equations
Solve the equation:
|2x - 6|- 1 = 4
x = 0. 5 and x = 5.5
Is the following sequence arithmetic, geometric, or neither:
-2 , 3, -4.5, 6.75
Sketch a graph to represent a linear, exponential, absolute value, and quadratic function.
Linear - Line
Exponential - Curve with an asymptote
Absolute Value - 'V'
Quadratic - Parabola or 'U'
A soccer team played 23 games during a season. The number of games they won was 4 less than 2 times the number of games they lost. How many games did the soccer team win during the season?
14
Find the domain and range of the following set:
{(9, 1) (-8, 0) (-1, 7) (0, 6) (-5, -7)}
D: {-8, -5, -1, 0, 9}
R: {-7, 0, 1, 6, 7}
The function f(x) is translated so that the new function can be represented by the function g(x) = f(x - 3) + 1. Describe the translation.
Shifted to the right 3, and up 1
Is this a function: {(1, 2), (2, 3), (3, 4), (4, 3)}
Yes
Solve the equation:
4|4x + 5|- 7 = 5
x = -2 and x = -0.5
Rewrite the following equation in terms of a:
ax + b = c
a = c - b / x
The equation of a is function f(x) = 2(3)x. What is the average rate of change of the function over the interval 2 < x < 4?
72
Which of the following is a solution to the inequality 0 > x2 + 5x - 6 ...
-10, -6, -3, 6
-3
Find the domain and range of the following function:
f(x) = 5(4)x
Domain: {all real numbers}
Range: {y > 0}
The function f(x) is transformed so that the new function can be represented by the function g(x) = 4f(x). Describe the transformation.
The function is compressed by a factor of 4
Write an equivalent expression:
(x3 + 4x2) - (5x2 - x)
x3 - x2 + x
Solve the following system of equations:
y = 4x - 5
y = -4x + 9
(1.75, 2)
Rewrite the following equation in terms of w:
3(6wr - 3) + 2r = 1
r = 5 / 9w + 1
You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per mile. Let m represent the number of miles ridden. Write an inequality to determine how many miles you can ride for $20.
5 + 2.50x < 20 (should be less than or equal to)
The function f(x) = -16x2 + 25x + 8.5 represents the velocity of tennis ball launched from a 1st floor balcony. What is a reasonable domain and range for this function.
D: { 0 < x < 1.85} the inequalities are supposed to include the 'equal to'
R: { 0 < y < 18.27} the inequalities are supposed to include the 'equal to'
In the transformed function af(x - h) + k describe the role of a, h, and k in transforming the function.
a = reflection, compression, stretch
h = horizontal shift
k = vertical shift
The mouse population is 25,000 and is decreasing in size at a rate of 20% per year. What is the growth rate and growth factor of this function?
Growth rate: 20% decrease
Growth factor: 0.8
Solve the following system of equations:
y = x2 + 4x + 4
y = -2x + 11
(-7, 25)
(1, 9)
Rewrite the following equation in terms of z:
x(y - z) - 2x(z + y) = xy
z = -2y / 3
In Lewis Carroll’s Through the Looking Glass, Tweedledum says, “The sum of your weight and twice mine is 361 pounds.” Tweedledee replies, “The sum of your weight and twice mine is 362 pounds.” Let x = the number of pounds Tweedledee weighs, and let y = the number of pounds Tweedledum weighs. Write a systems of equations that represents this situation.
x + 2y = 361
y + 2x = 362
The function f(x) = 3x2 is compared to the function g(x) = -0.75x2. Describe the domain and range of f(x) when compared to g(x).
The domain for both functions is all real numbers.
The range of f(x) is all real numbers greater than or equal to 0. While the range of g(x) is all real numbers less than or equal to 0.
The function f(x) = 2x2 is compared to the function g(x) = -0.5x2. Describe the impact of 'a' on these two functions.
g(x) is wider and reflected upside down when compared to f(x)
Solve the following compound inequality:
-15 < -2(x + 3) < -4
-1 < x < 4.5
Solve the equation:
2 - (3x - 4) + 7x = 2(4x + 1) - 9
x = 13/4
Find the 17th term in the following sequence:
-2, 7, 16, 25, ...
142
The length of a rectangular garden is 4 meters more than 3 times its width. The perimeter of the garden is 48 meters.
The length and width of the garden is ...
5 meters by 19 meters
What is the price per pound of the mixture?
$6.78