Modules 1-3 Review

Writing Equations

100

What do you use in an equation when a number is unknown?

A variable

200

How would you write "24 less than x"

x - 24

300

What does the word "yields" mean?

Equal to

400

How would you write "3 multiplied by the difference of x and 4"

3(x - 4)

500

The perimeter of a rectangular patio is 100 feet, the width of the patio is 8 feet, and the length is 3(x+2) feet. What is the equation to solve for x?

100 = 2(8) + 2(3(x+2))

Solving Equations

100

What does it mean to solve an equation?

To isolate the variable, find the value of the variable that makes the equation true

200

What are the 3 different possibilities for the number of solutions to an equation?

No solution, one solution, infinite solutions

300

Solve: x + 2 = -14 - x

x = -8

400

Solve: 3|y - 12| = 24

y = {4, 20}

500

How many solutions does the following equation have:

2x + 3(x - 2) = 6x - 2(x + 3) + x

Infinite solutions

Functions

100

For the ordered pair (6, 7), what is the y-value?

y = 7

200

What is the difference between a discrete vs. a continuous function?

A discrete function is individual points, a continuous function is a connected line or curve

300

What are all of the synonyms for independent variable?

Input, domain, x-value

400

If f(x) = x² - 3x + 1, what is f(4)?

f(4) = 5

500

Identify and interpret the y-intercept in the table of values

(0, 12). If you buys 12 pounds of shrimp, you can't buy any pounds of salmon. 

Rate of Change

100

If you have 2 different points, what should you label them to find the rate of change?

(x₁, y₁) and (x₂, y₂)

200

What is the formula for rate of change?

(y₂ - y₁)/(x₂ - x₁)

300

If a graph is measuring school attendance throughout the month of October and the rate of change is negative, what does that mean in the context of the situation?

Attendance is decreasing over time

400

Find the value of r if the rate of change between (6, r) and (5, -4) is -2. 

r = -6

500

For the graph of g(t), find the rate of change on the interval [1, 3]

rate of change = 2

Linear Functions

100

What is slope-intercept form?

y = mx + b

200

What is the difference between m and b in slope-intercept form? (be specific!)

m is the slope, it is how the line Moves between points

b is the y-intercept, it is where the line Begins on the y-axis

300

Describe the graph of y = -2x - 7

The graph has a y-intercept of (0, -7) and goes down 2 right 1 in between points

400

What is the equation of the line that has a slope of 5 and passes through the point (1, -2). 

y = 5x - 7

500

Convert to standard form: 

2x - 3y = 12

y = (2/3)x - 4