Drawing and reading function graphs
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Flip to reveal answersWhat does every point (x, y) on a function graph tell you?
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All 16 Flashcards โ Drawing and reading function graphs
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Question
What does every point (x, y) on a function graph tell you?
Answer
It tells you that when the input is x, the output is y โ i.e. f(x) = y. The x-axis shows inputs; the y-axis shows outputs.
Question
The graph of f passes through (3, 7). What is f(3)?
Answer
f(3) = 7. Read the y-value at x = 3 directly from the graph.
Question
How do you find f(4) from a graph?
Answer
Locate x = 4 on the horizontal axis, go straight up to the curve, then read across to the y-axis. That y-value is f(4).
Question
A graph passes through (0, โ5) and (4, 3). What is f(0)?
Answer
f(0) = โ5. The point (0, โ5) is on the graph, so when x = 0 the output is โ5.
Question
IB asks you to "sketch" a graph. What minimum features must you show?
Answer
Shape of the curve, any x- and y-intercepts, turning points (if present), and asymptotes (if relevant). Label key values. Accuracy matters less than the correct shape and labelled features.
Question
Which function families produce each shape: straight line, U-shape, J-curve, wave?
Answer
Straight line โ linear. U-shape โ quadratic. J-curve โ exponential. Wave โ sinusoidal.
Question
How do you sketch y = โ2x + 6?
Answer
y-intercept at (0, 6). Gradient = โ2: from (0, 6), go right 1 and down 2 to reach (1, 4). Draw a straight line through both points and label the y-intercept.
Question
A quadratic opens downward. What does this tell you about coefficient a?
Answer
a < 0. The parabola has a maximum (peak) at the vertex. If a > 0 it opens upward with a minimum.
Question
IB says "Write down f(2)." How do you answer from a graph?
Answer
Go to x = 2 on the horizontal axis, read straight up to the curve, then across to the y-axis. Write the y-value you find. "Write down" means no working is needed.
Question
From a graph, how do you find x when f(x) = 5?
Answer
Draw a horizontal line at y = 5. Where it meets the curve, read straight down to the x-axis. There may be more than one solution.
Question
A graph shows f(x) = 0 at x = โ1 and x = 3. What does this mean?
Answer
The function has two x-intercepts (zeros/roots) at x = โ1 and x = 3. The curve crosses the x-axis at those points.
Question
IB allows ยฑ0.2 tolerance when reading values from a graph. Why?
Answer
Printed graphs have limited precision. As long as your reading is within 0.2 of the true value, the mark is awarded. Always read as carefully as possible.
Question
How can you tell an exponential graph from a quadratic graph?
Answer
Exponential: approaches a horizontal asymptote (y โ 0 as x โ โโ), never crosses the x-axis (if a > 0). Quadratic: has a vertex (turning point), usually has two x-intercepts, is symmetric.
Question
A graph approaches y = 4 as x โ โ but never quite reaches it. What feature is this?
Answer
A horizontal asymptote at y = 4. The curve gets arbitrarily close but never equals 4.
Question
A function graph has two turning points. What types could it be?
Answer
A cubic polynomial or a sinusoidal function. A quadratic has only one turning point; two suggests a higher-degree polynomial or a periodic function.
Question
An exponential model y = a ยท bหฃ with b > 1 is graphed. As x โ โ, what happens to y?
Answer
y โ โ. The graph grows without bound โ steeper and steeper. As x โ โโ, y โ 0 (horizontal asymptote).
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Graph of a function
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