Algebra 2 Flashcards: Using Intersections To Solve Equivalent Functions
Study Using Intersections To Solve Equivalent Functions in Algebra 2 with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.
This deck focuses on Using Intersections To Solve Equivalent Functions, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.
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Algebra 2 Flashcards: Using Intersections To Solve Equivalent Functions
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QUESTION
Find the intersection x-value: f(x)=3x and g(x)=27.
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ANSWER
x=3. Set 3x=27=33, so x=3.
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Flashcard 1: Find the intersection x-value: f(x)=3x and g(x)=27.
Answer: x=3. Set 3x=27=33, so x=3.
Flashcard 2: What is the intersection x-value of f(x)=x3 and g(x)=0?
Answer: x=0. Set x3=0, so x=0.
Flashcard 3: What is the intersection x-value if f(x)=g(x) occurs at point (4,−3)?
Answer: x=4. Intersection coordinates give the solution x-value directly.
Flashcard 4: Which midpoint does bisection test first on the interval [2,6]?
Answer: x=4. Bisection starts at the midpoint of the interval.
Flashcard 5: Which interval brackets a solution if h(1)=−2 and h(2)=3 for h(x)=f(x)−g(x)?
Answer: A solution lies in (1,2). Sign change from negative to positive indicates a zero crossing.
Flashcard 6: Find the intersection x-value(s): f(x)=x2 and g(x)=−x2.
Answer: x=0. Set x2=−x2: 2x2=0, so x=0.
Flashcard 7: Find the intersection x-value(s): f(x)=x3 and g(x)=x.
Answer: x=−1, x=0, and x=1. Set x3=x and factor: x(x2−1)=x(x−1)(x+1)=0.
Flashcard 8: Find the intersection x-value: f(x)=ln(x) and g(x)=ln(5).
Answer: x=5. Set ln(x)=ln(5): x=5.
Flashcard 9: Identify the intersection x-value: f(x)=x and g(x)=x.
Answer: x=0 and x=1. Set x=x and square: x2=x, so x(x−1)=0.
Flashcard 10: Identify the valid solution of ln(x−2)=0: x=2 or x=3?
Answer: x=3. Only x=3 makes the argument x−2=1>0 valid.
Flashcard 11: Find the intersection x-value: f(x)=ln(x−2) and g(x)=0.
Answer: x=3. Set ln(x−2)=0: x−2=1, so x=3.
Flashcard 12: Find the intersection x-value: f(x)=10x and g(x)=1000.
Answer: x=3. Set 10x=1000=103, so x=3.
Flashcard 13: Find the intersection x-value: f(x)=ex and g(x)=1.
Answer: x=0. Set ex=1=e0, so x=0.
Flashcard 14: Find the intersection x-value: f(x)=ln(x) and g(x)=0.
Answer: x=1. Set ln(x)=0: x=e0=1.
Flashcard 15: Find the intersection x-value: f(x)=log(x) and g(x)=2.
Answer: x=100. Set log(x)=2: x=102=100.
Flashcard 16: Find the intersection x-value: f(x)=log2(x) and g(x)=5.
Answer: x=32. Set log2(x)=5: x=25=32.
Flashcard 17: Find the intersection x-value: f(x)=ln(x) and g(x)=1.
Answer: x=e. Set ln(x)=1: x=e1=e.
Flashcard 18: What is the typical graphical output used to approximate solutions to f(x)=g(x)?
Answer: The intersection point(s) of the two graphs. Graph intersections visually show where functions are equal.
Flashcard 19: Identify the intersection x-value: f(x)=2x+1 and g(x)=7.
Answer: x=3. Set 2x+1=7 and solve: 2x=6, so x=3.
Flashcard 20: Identify the intersection x-value: f(x)=3x−2 and g(x)=x+6.
Answer: x=4. Set 3x−2=x+6 and solve: 2x=8, so x=4.
Flashcard 21: Identify the intersection x-value: f(x)=−x+5 and g(x)=2x−1.
Answer: x=2. Set −x+5=2x−1 and solve: 6=3x, so x=2.
Flashcard 22: What are the intersection x-values of f(x)=x2 and g(x)=4?
Answer: x=−2 and x=2. Set x2=4 and solve: x=±4=±2.
Flashcard 23: What are the intersection x-values of f(x)=x2−1 and g(x)=0?
Answer: x=−1 and x=1. Set x2−1=0 and factor: (x−1)(x+1)=0.
Flashcard 24: What are the intersection x-values of f(x)=x2 and g(x)=x?
Answer: x=0 and x=1. Set x2=x and solve: x2−x=0, so x(x−1)=0.
Flashcard 25: Find the intersection x-values: f(x)=x2+2x and g(x)=0.
Answer: x=−2 and x=0. Set x2+2x=0 and factor: x(x+2)=0.
Flashcard 26: Find the intersection x-values: f(x)=x2−4x and g(x)=0.
Answer: x=0 and x=4. Set x2−4x=0 and factor: x(x−4)=0.
Flashcard 27: Find the intersection x-values: f(x)=∣x∣ and g(x)=2.
Answer: x=−2 and x=2. Set ∣x∣=2: x=2 or x=−2.
Flashcard 28: Find the intersection x-values: f(x)=∣x−1∣ and g(x)=3.
Answer: x=−2 and x=4. Set ∣x−1∣=3: x−1=3 or x−1=−3.
Flashcard 29: Find the intersection x-value(s): f(x)=∣x∣ and g(x)=x.
Answer: x≥0. When x≥0, ∣x∣=x, so they're equal.
Flashcard 30: Find the intersection x-value(s): f(x)=∣x∣ and g(x)=−x.