Functions Flashcards
Hyperbola formula? Give detail on what each part means
y = a/(x+p) + q
-> a = determines placement of graph:
(+a)=graph in 2nd & 4th quadrant
(-a)=graph in 1st & 3rd quadrant
-> q = vertical shift, horizontal asymptote
-> p = horizontal shift, vertical asymptote
Parabola/quadratic formula (turning point form)? Give detail on what each part means
y = a(x+p)2 +q
-> a= whether graph is ‘happy’ (+a) or ‘sad’ (-a)
-> p= horizontal shift (moving left for positive, right for negative)
-> q= vertical shift
Parabola/quadratic formula (root form)?
y = a (x-x1)(x-x2)
Parabola/quadratic formula (standard form)?
y = ax2 + bx + c
Exponential formula?
y = a . bx+p + q
Straight line formula?
y = mx+c
Mother function for straight line?
y=x
Mother function for parabola?
y=x2
Mother function for hyperbolas?
y=1/x
Mother function for exponential?
y=bx (b>1 OR 0<b<1)
How does one find equations of functions using points on the graph?
Substitute the points
How to find the turning point on a parabola?
- ensure that parabola equation is in TP form ( y = a((x+p)2+q )
- if not in this form, use completing the square (or shortcut -b/2a) to get it into TP form
- TP = (-p;q)
Finding x intercepts?
Make y=0
Finding y intercepts?
make x=0
Finding points of intersection?
Use simultaneous equations
Horizontal distance?
HD = xright - xleft
Vertical distance?
VD = ytop - ybottom
How to find average gradient? (for curves)
averagem=f(x2) - f(x1)/x2 - x1
How to find gradient?
Change in y over change in x
What are the transformations that can occur in a function?
- translation (shift up/down or left/right)
- reflection (across x/y axis)
- stretch/squash
Explain translations
Shifts.
In f(x) + q, added q value = vertical shift
In f(x + p), added p value = horizontal shift
Explain reflections.
Over x axis: -f(x) (entire equation x-1)
Over y axis: f(-x) (All values switch)
