Mathe Steckbriefaufgaben Klasse 11
Steckbriefaufgaben
Statement: function f Condition (s)
Is a completely rational function of grade 3 f(x)= ax3 + bx2 + cx + d
Is a completely rational function of grade n f(x)=anxn+ an-1xn-1+…+a2x2 + a1x1 + a0
Is symmetrical about the origin f(x) has only odd exponents
Is symmetrical about the y-axis f(x) has only even exponents
Passes through point A(1|2) f(1) = 2
f(-1) = 3
Has a minimum point at (-1|3)
f’(-1) = 0
Has a maximum point on the y-axis f’(0) = 0
Touches the x-axis at x = 5 f(5) = 0
f’’(-4) = 0
Has a point of inflection at W(-4|7)
f(-4) = 7
f(0) = 0
Has a point of inflection at the origin with the x-axis as a tangent
f’(0) = 0
(Wendetangente)
f’’(0) = 0
f(3) = 1
Has a tangent at point P(3|-1) that is parallel to the straight line
g’(x) = -3
g(x) = -3x + 7
f’(x) = -3
f’(2) = 0
Has a point of inflection with zero gradient at x = 2 (Sattelpunkt)
f’’(2) = 0
y = die Tangente für den Punkt x=1
y = 2*1 + 4 y = 6
Touches the straight line y = 2x + 4 at x = 1
f(1) = 6
f’(1) = 2
Has an x-intercept at x = -4 f(-4) = 0
Has a gradient of 3 at x = -1 f’(-1) = 3
Intersects the y-axis at y = 3 f(0) = 3
f’(2) = 1
Has a point of inflection at x = 2 with gradient 1
f’’(2) = 0
g’(x) = 2x g’(-3) = 2*(-3) = -6
Has at x = -3 the same gradient as g(x) = x2
f’(-3) = -6
1
Silke Redecker
Steckbriefaufgaben
Statement: function f Condition (s)
Is a completely rational function of grade 3 f(x)= ax3 + bx2 + cx + d
Is a completely rational function of grade n f(x)=anxn+ an-1xn-1+…+a2x2 + a1x1 + a0
Is symmetrical about the origin f(x) has only odd exponents
Is symmetrical about the y-axis f(x) has only even exponents
Passes through point A(1|2) f(1) = 2
f(-1) = 3
Has a minimum point at (-1|3)
f’(-1) = 0
Has a maximum point on the y-axis f’(0) = 0
Touches the x-axis at x = 5 f(5) = 0
f’’(-4) = 0
Has a point of inflection at W(-4|7)
f(-4) = 7
f(0) = 0
Has a point of inflection at the origin with the x-axis as a tangent
f’(0) = 0
(Wendetangente)
f’’(0) = 0
f(3) = 1
Has a tangent at point P(3|-1) that is parallel to the straight line
g’(x) = -3
g(x) = -3x + 7
f’(x) = -3
f’(2) = 0
Has a point of inflection with zero gradient at x = 2 (Sattelpunkt)
f’’(2) = 0
y = die Tangente für den Punkt x=1
y = 2*1 + 4 y = 6
Touches the straight line y = 2x + 4 at x = 1
f(1) = 6
f’(1) = 2
Has an x-intercept at x = -4 f(-4) = 0
Has a gradient of 3 at x = -1 f’(-1) = 3
Intersects the y-axis at y = 3 f(0) = 3
f’(2) = 1
Has a point of inflection at x = 2 with gradient 1
f’’(2) = 0
g’(x) = 2x g’(-3) = 2*(-3) = -6
Has at x = -3 the same gradient as g(x) = x2
f’(-3) = -6
1
Silke Redecker
