Pure

Question 1

Two distinct real root

Answer 1

b*2-4ac>0

Question 2

One repeated real root

Answer 2

b*2-4ac=0

Question 3

No real roots

Answer 3

b*2-4ac<0

Question 4

y=af(x)

Answer 4

Stretch graph in vertical direction by multiple of a

Question 5

y=f(ax)

Answer 5

Stretch graph on horizontal direction by multiple of 1/a

Question 6

y=-f(x)

Answer 6

Reflection of y=f( x) in x-axis

Question 7

y=f(-x)

Answer 7

Reflection of y=f(x) in y-axis

Question 8

Proof by exhaustion

Answer 8

Split statement into smaller cases and prove each case separately.

Question 9

Proof by counter example

Answer 9

Prove statement isn’t true by counter example

Question 10

Proof by contradiction

Answer 10

1. Assume given statement is false
2. We work to show this assumption leads to contradiction, either in assumption we made or fact we know to be true.
   *rational no.(a/b) and a and b are integers

Question 11

Algebraic division

Answer 11

F(x)\G(x)=Q(x)+r/G(x)
-Q(x): quotient. On the top part of the long division
-F(x): inside of long division
-G(x): outside of long division
-r: remainder

Question 12

Functions

Answer 12

1.One-to-One
2. Many-to-One
*Both functions as there is only one output

Question 13

Even functions

Answer 13

f(-x)=f(x) so y-axis is line of symmetry