A table that represents the transformation of f given by g should be written as follows;
x -3 -1 1 3
g(x) -15 -3 9 21
In Mathematics and Euclidean Geometry, a function can be stretched or compressed by multiplying it with a numerical value that is either greater than 1 or less than -1 respectively.
Based on the information provided above, we can logically deduce that the parent function, f(x) was vertically stretched by a factor of 3, in order to produce the transformed function;
g(x) = 3f(x)
In order to create a table of values for g(x), we would multiply the f(x) values by 3 as follows;
g(-3) = 3 × f(-3)
g(-3) = 3 × -5
g(-3) = -15
g(-1) = 3 × f(-1)
g(-1) = 3 × -1
g(-1) = -3
g(1) = 3 × f(1)
g(1) = 3 × 3
g(1) = 9
g(3) = 3 × f(3)
g(3) = 3 × 7
g(3) = 21