Algebra Mid-Chapter 2 Review

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Questions and Answers

State the domain of {(1, 2), (3, 4), (5, 6), (7, 8)}.

{1, 3, 5, 7}

State the range of {(1, 2), (3, 4), (5, 6), (7, 8)}.

{2, 4, 6, 8}

Find f(4) if f(x) = -3x + 2.

-10

Find f(0) if f(x) = -3x + 2.

2 Signup and view all the answers

Find f(-a) if f(x) = -3x + 2.

3a + 2 Signup and view all the answers

Is 3x + 4y = 12 linear or nonlinear?

Linear Signup and view all the answers

Is y = x³ - 6 linear or nonlinear?

Nonlinear Signup and view all the answers

Write the equation in standard form: -4y = 3x - 24.

3x + 4y = 24 Signup and view all the answers

Write the equation in standard form: y = 12x.

12x - y = 0 Signup and view all the answers

Find the slope of the line that passes through (2, 5) and (6, -3).

-2 Signup and view all the answers

Find the slope of the line that passes through (8, 2) and (2, 8).

-1 Signup and view all the answers

What does m represent?

slope Signup and view all the answers

What does b represent?

y-intercept Signup and view all the answers

Write an equation in slope-intercept form that satisfies the conditions: slope -2, passes through (-3, -5).

y = -2x - 11 Signup and view all the answers

Write an equation in slope-intercept form that satisfies the conditions: passes through (-2, 4) and (0, 8).

y = 2x + 8 Signup and view all the answers

Write an equation in slope-intercept form that satisfies the conditions: passes through (3, 5) and (-1, 5).

y = 5 Signup and view all the answers

Parallel lines have the ___________ slope.

same Signup and view all the answers

Perpendicular lines have the _____________ slope.

opposite reciprocal Signup and view all the answers

Find the slope of the line parallel to y = 3x + 5.

3 Signup and view all the answers

Find the slope of the line perpendicular to y = 3x + 5.

-1/3 Signup and view all the answers

Study Notes

Domain and Range

The domain of a set of ordered pairs consists of the first elements: {1, 3, 5, 7}.
The range consists of the second elements from the same set: {2, 4, 6, 8}.

Function Evaluation

For the function f(x) = -3x + 2:
- f(4) results in -10.
- f(0) results in 2.
- f(-a) results in 3a + 2.

Linearity

The equation 3x + 4y = 12 is classified as linear.
The equation y = x³ - 6 is classified as nonlinear.

Standard Form

The equation -4y = 3x - 24 can be rearranged to standard form as 3x + 4y = 24.
The equation y = 12x can be converted to standard form as 12x - y = 0.

Slope Calculation

The slope between the points (2, 5) and (6, -3) is calculated as -2.
The slope between the points (8, 2) and (2, 8) is calculated as -1.

Key Definitions

The symbol m represents slope.
The symbol b denotes the y-intercept.

Slope-Intercept Form

An equation with a slope of -2 through the point (-3, -5) is expressed as y = -2x - 11.
An equation passing through (-2, 4) and (0, 8) has the form y = 2x + 8.
A horizontal line with points (3, 5) and (-1, 5) is represented as y = 5.

Relationships Between Slopes

Parallel lines maintain the same slope.
Perpendicular lines have slopes that are opposite reciprocals.

Slope of Parallel and Perpendicular Lines

A line parallel to y = 3x + 5 has a slope of 3.
A line perpendicular to y = 3x + 5 has a slope of -1/3.

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Description

Test your understanding of key algebraic concepts with this mid-chapter 2 quiz. Questions cover topics such as domain, range, and function evaluation. Perfect for reinforcing the material you have learned so far.