📈Functions

17 tricks available.

High school📈Functions
🎯
Sum and product of roots: S = −b/a, P = c/a
For ax²+bx+c=0, the roots satisfy x₁+x₂ = −b/a and x₁·x₂ = c/a. Handy without the discriminant.
High school📈Functions
📏
Tangent line equation: y = f'(a)(x − a) + f(a)
The tangent at a has slope f'(a) and passes through (a, f(a)). One formula, everything's in it.
High school📈Functions
📊
Successive percentage changes: the +10% then −10% trap
+10% then −10% does NOT bring you back to the starting price. The multiplier trick that fixes this in 3 seconds.
High school📈Functions
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Sign table: the method that organizes everything
Study the sign of $f(x)$, solve $f(x) > 0$, understand inequalities: one tool for all these questions.
High school📈Functions
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Sign of a quadratic: 'sign of a except between the roots'
ax² + bx + c has the sign of a, except between the roots. One sentence, whole sign chart.
High school📈Functions
🔢
Nth term of a sequence: the two formulas you must never forget
Arithmetic or geometric sequence: find the n-th term in 5 seconds with the right formula and zero index mistakes.
High school📈Functions
🧮
Quadratic equation: the discriminant in 5 seconds
$\Delta = b^2 - 4ac$. Three cases, three scenarios. The universal method for all $ax^2 + bx + c = 0$.
High school📈Functions
🎯
Product or quotient inequality: the sign chart is enough
Factor, sign chart for each factor, product of signs. One method that cracks them all.
Middle school📈Functions
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Linear function y = ax + b: all you need to know
a = slope, b = y-intercept. Two numbers, one line, a thousand problems solved.
High school📈Functions
📈
Inverse and square functions: variations and graphs
f(x) = 1/x and f(x) = x². Domain, variations, symmetries, graphs on one sheet.
High school📈Functions
📈
Homographic function: (ax+b)/(cx+d) and its hyperbola
f(x) = (ax+b)/(cx+d). Domain ℝ − {−d/c}, vertical and horizontal asymptotes, curve = shifted hyperbola.
High school📈Functions
🪞
Even and odd functions: the 2 symmetries to know
f(−x) = f(x): even (y-axis). f(−x) = −f(x): odd (origin). Two tests, two pictures.