Learn all concepts on graphs which are asked in SAT Test.

1. All about SAT Graphs
- FABMARKS -

2. GRAPHS on the SAT:
Function/EQUATION GRAPH
Linear LINE
Quadratic PARABOLA
Exponential EXPONENTIAL
Other Polynomial GRAPH

3. LINEAR EQUATION/FUNCTIONS – GRAPHS
A graph of a linear equation y=mx+c is a line on the coordinate plane with slope ‘m’
Slanting Up from left to right if m>0
Down from left to right if m<0
Ex: Y=3x-1 is a linear equation with slope of 3 (>0)
Points lying on the line:
X Y
-2 -7
-1 -4
0 -1
1 2
2 5

4. QUADRATIC EQUATION/FUNCTIONS – GRAPHS
A graph of a quadratic equation y=ax2+bx+c is a parabola on the coordinate plane
Opens: UP & has a min. value if a>0
& at x=-b/2a
DOWN & has a max. value if a<0
Ex: Y=2x2-x+1 is a quadratic equation opening up as a=2 (>0)
Points lying on the Parabola:
X Y
-2 11
-1 4
0 1
1 2
2 7

5. COMMON POINTS ABOUT GRAPHS
1. X intercept : Where the graph intersects the X axis (values of x when y=0)
2. Y intercept : Where the graph intersects the Y axis (values of y when x=0)
3. Zeroes/Roots/Solutions : Where the graph intersects the X axis (values of x when y=0)
4. X to Y mapping : For any value of x there is no more than 1 value of y
5. TRANSFORMATION OF GRAPHS  NEXT SLIDE

6. TRANSFORMATION OF GRAPHS
1. F(x) to F(x + a) Shifts the graph ‘a’ units right(if ‘-a’) or left(if ‘+a’)
(where a>0)
2. F(x) to F(x) + a Shifts the graph ‘a’ units UP (if ‘+a’) or DOWN (if ‘-a’)
(where a>0)
3. F(x) to F(-x) Reflects the graph with respect to the Y axis
4. F(x) to -F(x) Reflects the graph with respect to the X axis

7. 5. F(x) to F(ax) HORIZONTAL COMPRESSION/EXPANSION
if a>1 & 0<a<1
6. F(x) to a*F(x) VERTICAL EXPANSION/COMPRESSION
if a>1 & 0<a<1

8. SOME PRACTICE
1. If f(x) = -px2 + 3 is a function represented by the graph shown,
then what is the value of p+1?

9. SOME PRACTICE
2. If the graph shown is a representation of the function f(x) , which
of the following could be the representation of f(x-2) ?
A) B)
C) D)