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?
- 5 (correct)
- 10
- 7
- 3
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|?
- Vertical stretch by a factor of 3
- Reflected over the x-axis
- Translated down 5 units (correct)
- Translated right 4 units
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?
- an = -2n + 10
- an = -2n + 8
- an = 2n + 4
- an = -2n + 12 (correct)
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)?
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).
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?
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?
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?
What is the value of $g(6)$ if $g(6) = 12$?
What is the value of $g(6)$ if $g(6) = 12$?
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 ${-3, 0, 4}$?
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 $(4, 6)$.
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 $f(x) = |x|$?
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 $(4, 5)$?
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 $g(x) = x^2 + 3$?
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?
What does the inequality $-5y > -2y + 9$ simplify to?
What does the inequality $-5y > -2y + 9$ simplify to?
Flashcards
Function Value (f(x))
Function Value (f(x))
The output of a function for a given input value, represented as f(x), where x is the input.
Translation
Translation
A transformation that shifts the graph of a function horizontally or vertically.
Stretch or Compression
Stretch or Compression
A transformation that stretches or compresses the graph of a function either vertically or horizontally.
Reflection
Reflection
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Function
Function
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Domain
Domain
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Range
Range
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Linear Function
Linear Function
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Nonlinear Function
Nonlinear Function
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Slope
Slope
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Function Evaluation (f(x))
Function Evaluation (f(x))
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Vertical Translation
Vertical Translation
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Vertical Stretch or Compression
Vertical Stretch or Compression
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Horizontal Translation
Horizontal Translation
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Reflection over the y-axis
Reflection over the y-axis
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Arithmetic Sequence
Arithmetic Sequence
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Slope of a Line
Slope of a Line
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Equation of a Line
Equation of a Line
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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.
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