Podcast
Questions and Answers
What is the value of f(4) if the number of people at a tourist destination at that time is 5?
What is the value of f(4) if the number of people at a tourist destination at that time is 5?
Which transformation is NOT applied to the function h(x) = -3|x - 4| + 5 relative to the parent function f(x) = |x|?
Which transformation is NOT applied to the function h(x) = -3|x - 4| + 5 relative to the parent function f(x) = |x|?
What is the nth term of the arithmetic sequence 10, 8, 6, 4?
What is the nth term of the arithmetic sequence 10, 8, 6, 4?
What is the slope of the line passing through the points (-3, 5) and (3, 6)?
What is the slope of the line passing through the points (-3, 5) and (3, 6)?
Signup and view all the answers
Find the equation of the line with a slope of 1/2 and passing through the point (4, 2).
Find the equation of the line with a slope of 1/2 and passing through the point (4, 2).
Signup and view all the answers
If Sarah's August bill was $45 for 150 minutes, how much did she pay per minute?
If Sarah's August bill was $45 for 150 minutes, how much did she pay per minute?
Signup and view all the answers
What inequality represents the number of candy bags (x) and cookie bags (y) needed to raise at least $600?
What inequality represents the number of candy bags (x) and cookie bags (y) needed to raise at least $600?
Signup and view all the answers
What is the answer to the expression 4[f(-2) + h(3)] if f(x) = 3x + 2 and h(x) = x² - 1?
What is the answer to the expression 4[f(-2) + h(3)] if f(x) = 3x + 2 and h(x) = x² - 1?
Signup and view all the answers
What is the value of $g(6)$ if $g(6) = 12$?
What is the value of $g(6)$ if $g(6) = 12$?
Signup and view all the answers
What is the range of the function $g(x) = x^2 - x + 2$ for the domain ${-3, 0, 4}$?
What is the range of the function $g(x) = x^2 - x + 2$ for the domain ${-3, 0, 4}$?
Signup and view all the answers
Determine the equation of the line that passes through the points $(0, 2)$ and $(4, 6)$.
Determine the equation of the line that passes through the points $(0, 2)$ and $(4, 6)$.
Signup and view all the answers
What transformation occurs with the function $k(x) = 4|x + 2| - 7$ relative to $f(x) = |x|$?
What transformation occurs with the function $k(x) = 4|x + 2| - 7$ relative to $f(x) = |x|$?
Signup and view all the answers
What is the slope of the line passing through the points $(-2, -1)$ and $(4, 5)$?
What is the slope of the line passing through the points $(-2, -1)$ and $(4, 5)$?
Signup and view all the answers
What is the result of $3[f(1) + g(2)]$ given $f(x) = 5x - 4$ and $g(x) = x^2 + 3$?
What is the result of $3[f(1) + g(2)]$ given $f(x) = 5x - 4$ and $g(x) = x^2 + 3$?
Signup and view all the answers
What is the base fee if the total cost of a 10-mile trip is $30 with a charge of $2.50 per mile?
What is the base fee if the total cost of a 10-mile trip is $30 with a charge of $2.50 per mile?
Signup and view all the answers
What does the inequality $-5y > -2y + 9$ simplify to?
What does the inequality $-5y > -2y + 9$ simplify to?
Signup and view all the answers
Study Notes
Module 3: Relations and Functions
- Problem 1: Given a graph of temperature vs. time, find 𝑔(6). Answer: 𝑔(6) = 12.
- Problem 2: Transformations of 𝑘(𝑥) = 4|𝑥 + 2| – 7 relative to 𝑓(𝑥) = |𝑥|: Vertical stretch by a factor of 4, translated left 2 units, translated down 7 units.
- Problem 3: Given 𝑓(𝑥) = 5𝑥 – 4 and 𝑔(𝑥) = 𝑥² + 3, find 3[𝑓(1) + 𝑔(2)]: Answer: 30.
- Problem 4: Given 𝑓(𝑥) = 3𝑥 – 2, find 𝑓(5) – 𝑓(1): Answer: 12.
- Problem 5: Find the range of 𝑔(𝑥) = 𝑥² – 𝑥 + 2 for the domain {–3, 0, 4}: Answer: {8, 2, 14}.
- Problem 6: Given a graph of speed vs. time, find 𝑓(10): Answer: 𝑓(10) = 20.
- Problem 7: Transformations of 𝑚(𝑥) = –|𝑥 – 5| + 3 relative to 𝑓(𝑥) = |𝑥|: Reflected over the x-axis, translated right 5 units, translated up 3 units.
Module 4: Linear and Nonlinear Functions
- Problem 8: Find the nth term of the arithmetic sequence 15, 12, 9, 6: Answer: 𝑎𝑛 = –3𝑛 + 18.
- Problem 9: Find the slope of the line through (–2, –1) and (4, 5): Answer: 1.
- Problem 10: Find the slope of the line through (2, 3) and (5, 3): Answer: 0.
- Problem 11: Find the equation of the line graphed, given points (0, 2) and (4, 6): Answer: 𝑦 = 𝑥 + 2.
Module 5: Creating Linear Equations
- Problem 16: A taxi service charges $2.50 per mile plus a base fee. If a 10-mile trip costs $30, find the base fee: Answer: $5. Find the cost of a 20-mile trip: Answer: $55.
- Problem 17: Find the equation of a line with a slope of 3 and passing through (–1, –5): Answer: 𝑦 = 3𝑥 – 2.
Module 6: Linear Inequalities
- Problem 24: Solve –3𝑦 ≤ 12: Answer: 𝑦 ≥ –4.
- Problem 25: Identify inequalities with no solution (examples needed).
- Problem 26: Sara sells T-shirts ($10 each) and mugs ($5 each) to raise at least $200. Write the inequality for the number of T-shirts (x) and mugs (y): Answer: 10𝑥 + 5𝑦 ≥ 200.
- Problem 27: Solve –5𝑦 > –2𝑦 + 9: Answer: 𝑦 < 3.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers concepts from Module 3 and Module 4, focusing on relations and functions. It includes problems related to transformations, finding specific function values, calculating slopes, and analyzing sequences. Test your understanding of mathematical functions and their applications.
