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All 16 Flashcards — x-intercepts and y-intercepts
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Question
Define x-intercept and y-intercept.
Answer
x-intercept: where the graph crosses the x-axis — this is where y = 0. y-intercept: where the graph crosses the y-axis — this is where x = 0.
Question
Can a function have more than one y-intercept?
Answer
No. A function produces exactly one output for x = 0, so there is exactly one y-intercept. However, a function can have zero, one, or many x-intercepts.
Question
A function has no x-intercept. What does this tell you about the graph?
Answer
The curve stays entirely above or below the x-axis — its output is never zero.
Question
IB uses the words "zeros", "roots", and "x-intercepts." What do they all mean?
Answer
All three refer to the values of x where f(x) = 0 — i.e. where the graph meets the x-axis. They are the same thing.
Question
How do you find the y-intercept of any function algebraically?
Answer
Substitute x = 0 into the function and calculate the output. The y-intercept is at the point (0, f(0)).
Question
Find the y-intercept of f(x) = x² − 3x + 7.
Answer
f(0) = 0 − 0 + 7 = 7. y-intercept is (0, 7).
Question
State the y-intercept of f(x) = 5 · 2ˣ.
Answer
f(0) = 5 · 2⁰ = 5 · 1 = 5. y-intercept is (0, 5). For any exponential y = a · bˣ, the y-intercept is always (0, a).
Question
Why is the y-intercept always the constant c in y = mx + c?
Answer
When x = 0: y = m(0) + c = c. So the line always meets the y-axis at the constant term.
Question
How do you find x-intercepts algebraically?
Answer
Set f(x) = 0 and solve. Each solution is an x-intercept (root/zero).
Question
Find the x-intercepts of f(x) = x² − x − 6.
Answer
Set x² − x − 6 = 0. Factor: (x − 3)(x + 2) = 0. So x = 3 or x = −2. x-intercepts are (3, 0) and (−2, 0).
Question
On Paper 2, IB asks "Find the zeros of f." What do you write?
Answer
The x-values where f(x) = 0, typically as coordinates: e.g. (−2, 0) and (3, 0), or just x = −2 and x = 3. Using the GDC Zero function is fine.
Question
A quadratic discriminant b² − 4ac < 0. What does this mean for x-intercepts?
Answer
No real x-intercepts — the parabola is entirely above or below the x-axis. The equation has no real solutions.
Question
The model h(t) = −5t² + 20t gives the height (m) of a ball. What do the x-intercepts represent?
Answer
Times when h = 0 — i.e. when the ball is on the ground: t = 0 (launch) and t = 4 (lands). x-intercepts are times, not heights.
Question
P(t) = 800 · 1.04ᵗ. What does the y-intercept represent?
Answer
P(0) = 800. The y-intercept is the initial population of 800 (at time t = 0).
Question
IB asks "State the meaning of the y-intercept in this context." How do you score the mark?
Answer
State what the y-intercept value represents using the context's real-world units and language. E.g. "800 is the initial population at the start of the study."
Question
C(n) = 120n + 400. What does the y-intercept 400 represent?
Answer
The fixed cost of 400 — even if n = 0 units are produced, the cost is still 400 (overhead/startup cost).
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