Functions

Question 0

Odd Functions

Answer 0

F(-x)=-F(x)

Symmetrical 180 degrees about the origin

Question 1

Even functions

Answer 1

F(-x)=F(x)

Symmetrical about the y-axis

Question 2

Increasing or decreasing sections of a function

Answer 2

1) if m>0 the function is increasing
2) if m<0 the function is decreasing
3) if m=0 the function is stationary

Question 3

Circles

Answer 3

The equation of a circle with centre (a,b) and a radius r is given by
(x-a)^2+(y-b)^2=r^2

Question 4

Semi circles

Answer 4

Y is equal to plus (positive) minus (negative) r squared minus x squared

Question 5

Absolute value graphs

Answer 5

Y is equal to the absolute value of (mx+a) plus b WHERE:

1) m is a constant representing the gradient
2) a is a constant- set mx+a=0 to find the midline of the graph
3) b is a constant representing the imaginary y-line the ab graph sits on

Question 6

Graphing absolute values

Answer 6

Method 1
Find m, a and b
Method 2 (harder ab’s eg x outside absolute value)
Find the positive and negative cases and graph each line
Test top or bottom half

Question 7

Solving AB equations graphically

Answer 7

*Hint
LHS=RHS    ON
LHS>RHS    ABOVE
LHS<RHS    BELOW 
Graph both the absolute value and the RHS graph and use the rules above to highlight the lines

Question 8

Exponential function (rocket ship)

Answer 8

y=a^x +b

Question 9

Hyperbolas (starfish)

Answer 9

y=a/(x+b) + c

where c is the horizontal asymptote and b is the vertical (set (x+b)=0))

Question 10

Cubic functions (hourglass)

Answer 10

y=ax^3 +b

Question 11

Sketching inequations

Answer 11

• Requires testing
  1) greater than or less than dotted line
  2) greater than or equal to and less than or equal two solid line

Question 12

Limits

Answer 12

To find a limit you must sub in the value x approaches for every x value.

Question 13

Special Limit

Answer 13

A special limit is limit as x goes to infinity 1/x is equal to zero.
*the key to these limits is to divide each term by the x-value that has the highest power and then simplify such that any term that has x on the denominator will equal to zero.

Question 14

Oblique

Answer 14

An oblique asymptote occurs when the highest power of x is higher on the numerator than denominator.
*Finding the oblique asymptote
Use the division of polynomials to find the oblique asymptote. Divide the numerator by the denominator and the quotient is the asymptote.

Question 15

Further graphing

Answer 15

*Intercepts
The x-intercept occurs when y=0
The y-intercept occurs when x=0
*even and odd functions
*asymptotes/limits
*domain and range

Question 16

Finding domain and range

Answer 16

Domain: when finding domain look for the x values that are impossible
E.g. 1/x x cannot equal to zero, root x is greater than or equal to zero
Range: when finding range, look for results of different x values including positive, negative, and zero values