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SAT Math
4. Functions and Graphs
Written by: Pranav I
Formatted by: Rithanya S
- Functions are a machine for producing ordered pairs
- An input value (x) goes into the function machine
- An output value (y) comes out of the function machine
- f(x)=y
- When the input of a function is given, use the Plugging In method
- When the output of a function is given, use the PITA method
- A word problem describing a function might ask the test taker to build a function
- Some function questions might also include percentages
- Other questions will have the input and output values of a function in a table
- Functions are just another way to express graphs!
- The coordinate plane, or the xy-plane, is made up of two number lines that intersect at a right angle
- The horizontal number line is called the x-axis and the vertical number line is the y-axis
- The four areas (numbered counterclockwise ; starting from the top right) formed by the intersection of the axes are called quadrants
- The point (0,0) is called the origin and is the intersection of the axes
Points on a line
- Plug in the coordinates of the point into the equation of the line, if that point makes the equation a true statement, it is on the line and vice versa.
Slope
- Slope is the rate of change of a line and is commonly known as rise over run
- It is denoted by the letter m
Equations of a line
Slope-Intercept Form
- y=mx+c
- c is the y-intercept and m is the slope
- y-intercept is the point where the function crosses the y-axis
Standard Form
- Ax + By = C
- A, B and C are constants ; A and B do not equal zero
Parallel and Perpendicular Lines
- Parallel lines have the same slope ; they never intersect
- Perpendicular lines have a slope that is the negative reciprocal of the other line’s slope ; they intersect in a single point at a right angle
