Functions

Question 1

Hyperbola formula? Give detail on what each part means

Answer 1

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

Question 2

Parabola/quadratic formula (turning point form)? Give detail on what each part means

Answer 2

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

Question 3

Parabola/quadratic formula (root form)?

Answer 3

y = a (x-x₁)(x-x₂)

Question 4

Parabola/quadratic formula (standard form)?

Answer 4

y = ax² + bx + c

Question 5

Exponential formula?

Answer 5

y = a . b^x+p + q

Question 6

Straight line formula?

Answer 6

y = mx+c

Question 7

Mother function for straight line?

Answer 7

y=x

Question 8

Mother function for parabola?

Answer 8

y=x²

Question 9

Mother function for hyperbolas?

Answer 9

y=1/x

Question 10

Mother function for exponential?

Answer 10

y=b^x (b>1 OR 0<b<1)

Question 11

How does one find equations of functions using points on the graph?

Answer 11

Substitute the points

Question 12

How to find the turning point on a parabola?

Answer 12

• 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)

Question 13

Finding x intercepts?

Answer 13

Make y=0

Question 14

Finding y intercepts?

Answer 14

make x=0

Question 15

Finding points of intersection?

Answer 15

Use simultaneous equations

Question 16

Horizontal distance?

Answer 16

HD = x_right - x_left

Question 17

Vertical distance?

Answer 17

VD = y_top - y_bottom

Question 18

How to find average gradient? (for curves)

Answer 18

average_m=f(x₂) - f(x₁)/x₂ - x₁

Question 19

How to find gradient?

Answer 19

Change in y over change in x

Question 20

What are the transformations that can occur in a function?

Answer 20

• translation (shift up/down or left/right)
• reflection (across x/y axis)
• stretch/squash

Question 21

Explain translations

Answer 21

Shifts.
In f(x) + q, added q value = vertical shift
In f(x + p), added p value = horizontal shift

Question 22

Explain reflections.

Answer 22

Over x axis: -f(x) (entire equation x-1)
Over y axis: f(-x) (All values switch)