Reading the graph of a function
Reading a curve: image, preimage, extremum, direction of variation, slope between two points, graphical solving of f(x) = k and f(x) ≥ k, then going from the curve to the table of variations.
- 26 cards
- 7 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- The curves
- Scenarios
- Understand
A few cards from the deck
Preimage: what is it?
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For a real y, any real x such that f(x) = y. On the curve, it is the x-coordinate of a point of height y.
A real x has at most one image, but a real y can have several preimages, or none: on the parabola of x², 4 has two (−2 and 2) and −1 has none.
The point (2, 5) lies on the curve of f. Which of these statements is correct?
- f(2) = 5
- f(5) = 2
- 2 is the image of 5
- 5 is a preimage of 2
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f(2) = 5
The point (a, b) means f(a) = b: b is the image of a, and a is a preimage of b. The three decoys swap the roles of the x- and y-coordinates.
The solutions of f(x) = k are the x-coordinates of the intersection points of the curve with the horizontal line y = ….
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The solutions of f(x) = k are the x-coordinates of the intersection points of the curve with the horizontal line y = k.
Start on the y-axis at height k, draw the horizontal, and read the x-values of the points where it meets the curve. There can be zero, one or several solutions.