Standard functions
The reference functions: affine, square, cube, inverse, square root, absolute value, exponential, logarithms, sine and cosine. Domain, shape, variations, special values, algebraic properties and the effect of a shift on the curve.
- 28 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
Domain: what is it?
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The set of real numbers x for which the expression of f(x) can be computed.
Three reflexes: a denominator is not zero, a square-root argument is zero or positive, a logarithm's argument is strictly positive.
What is the domain of f(x) = ln(x − 3)?
- (3, +∞)
- [3, +∞)
- (−∞, 3)
- ℝ without 3
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(3, +∞)
We need x − 3 > 0, so x > 3, bound excluded: ln(0) does not exist. The domain of ln x itself is (0, +∞); here the argument is shifted by 3.
The curve of an affine function x ↦ mx + p is a …; that of a quadratic function x ↦ ax² + bx + c is a ….
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The curve of an affine function x ↦ mx + p is a line; that of a quadratic function x ↦ ax² + bx + c is a parabola.
m is the slope and p the y-intercept. For the parabola, the sign of a gives the direction: branches up if a > 0, down if a < 0.