Podcast
Questions and Answers
State the domain of {(1, 2), (3, 4), (5, 6), (7, 8)}.
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)}.
State the range of {(1, 2), (3, 4), (5, 6), (7, 8)}.
{2, 4, 6, 8}
Find f(4) if f(x) = -3x + 2.
Find f(4) if f(x) = -3x + 2.
-10
Find f(0) if f(x) = -3x + 2.
Find f(0) if f(x) = -3x + 2.
Find f(-a) if f(x) = -3x + 2.
Find f(-a) if f(x) = -3x + 2.
Is 3x + 4y = 12 linear or nonlinear?
Is 3x + 4y = 12 linear or nonlinear?
Is y = x³ - 6 linear or nonlinear?
Is y = x³ - 6 linear or nonlinear?
Write the equation in standard form: -4y = 3x - 24.
Write the equation in standard form: -4y = 3x - 24.
Write the equation in standard form: y = 12x.
Write the equation in standard form: y = 12x.
Find the slope of the line that passes through (2, 5) and (6, -3).
Find the slope of the line that passes through (2, 5) and (6, -3).
Find the slope of the line that passes through (8, 2) and (2, 8).
Find the slope of the line that passes through (8, 2) and (2, 8).
What does m represent?
What does m represent?
What does b represent?
What does b represent?
Write an equation in slope-intercept form that satisfies the conditions: slope -2, passes through (-3, -5).
Write an equation in slope-intercept form that satisfies the conditions: slope -2, passes through (-3, -5).
Write an equation in slope-intercept form that satisfies the conditions: passes through (-2, 4) and (0, 8).
Write an equation in slope-intercept form that satisfies the conditions: passes through (-2, 4) and (0, 8).
Write an equation in slope-intercept form that satisfies the conditions: passes through (3, 5) and (-1, 5).
Write an equation in slope-intercept form that satisfies the conditions: passes through (3, 5) and (-1, 5).
Parallel lines have the ___________ slope.
Parallel lines have the ___________ slope.
Perpendicular lines have the _____________ slope.
Perpendicular lines have the _____________ slope.
Find the slope of the line parallel to y = 3x + 5.
Find the slope of the line parallel to y = 3x + 5.
Find the slope of the line perpendicular to y = 3x + 5.
Find the slope of the line perpendicular to y = 3x + 5.
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.
