Functions Flashcards
(14 cards)
Where does the hyperbola xy=c^2 intersect the line y=x?
(c,c) and (-c,-c)
The circle x^2 +y^2 = r^2 has centre the origin and radius r. The circle is shifted so that its centre is at C(h,k). The point P(x,y) lies on the circle with centre C(h,k) and radius r. That is, P lies on the shifted circle in part a. This time, use the distance formula to find the radius PC to obtain the equation of the circle.
(x-h)^2 + (y-k)^2 = r^2
Let f(x) = 2x+3 and g(x) = ax+b, where b is a constant.
Find the values of a and b so that g(f(x)) = x, for all x.
a = 1/2
b = -3/2
A (1,4) B(-2,-3) C(8.5,-1.5) D(a,5.5) are the vertices of a parallelogram. Find the gradient of the diagonal BD
m=17/27
∣x−5∣+∣x−3∣=x^2-7
-5 , 3
|1/x| < 1
x<-1, x>1
How do you know if an inverse function exists for f(x)
Horizontal line test
An inverse function will exist for f(x) if the graph of f(x) passes the horizontal line test. If any horizontal line passes through a function only once, then the inverse of that function will pass the vertical line test, meaning that it is a function.
Remainder Theorem?
f(x)/(x-a) has a remainder of f(a)
Sum of roots for cubic?
α+β+γ = -b/a
Product of roots of cubic?
αβγ = -d/a
Sum of product of roots, 2 at a time (Cubic Polynomial)
αβ+βγ+αγ = c/a
α²+β²+γ²
(α+β+γ)² - 2(αβ+βγ+αγ)
A quadratic has roots α and β. What is the sum of the roots.
(α+β)=
-b/a
A quadratic has roots α and β. What is the product of the roots.
(αβ)=
c/a
