SAT Math Level 2 - FUNCTIONS

Question 1

Vertical Line Test

Answer 1

to test visually if a graph represents a function

Pass a vertical line from left to right over the graph of f(x). If the line intersects the curve in two or more places at the same time, then f(x) is NOT a function

Question 2

Function domains

Answer 2

The domain of a function is the set of x-values that we use as inputs

• Unless you are told otherwise, we make the domain include every x-value possible
  etc. the domain of f(t) = log(t - 4) is t > 4 because you cannot take the log of a negative number or zero

Question 3

Function range

Answer 3

The range of a function is the set of output values that the function takes as we input values from the domain
- If we are using the usual x and y variables, the range is the set of y-values for a given domain of x-values

Question 4

Geometrical Inverses

Answer 4

To get the graph of inverse of a function, just REFLECT the graph of f(x) in the line y = x

Question 5

Horizontal Line Test

Answer 5

Pass a horizontal line from down to up over the graph of f(x). If the line intersects the curve in two or more places at the same time, then f(x) doesn’t have an inverse that is also a function

Question 6

Even symmetry functions

Answer 6

A function has even symmetry if you reflect it in the y-axis and it looks exactly the same as before. This means f(x) = f(-x)

Question 7

Odd symmetry functions

Answer 7

A function has odd symmetry if you rotate it 180 degrees about the origin and it looks exactly the same as before. This means f(x) = -f(-x)

Question 8

Change f(x) to | f(x) | for a partial reflection in the x-axis

Answer 8

Only reflects parts of the graph below the x-axis. Keep the other parts fixed

Question 9

Change f(x) to f( | x | ) for a partial reflection in the x-axis

Answer 9

A tad strange. DELETE ALL THE GRAPH for x < 0, keeping the right hand piece. KEEPING THIS FIXED, reflect it in the y-axis