Question

Determine the graph for each g (x) function if the parent function is f(x) = x. Graph both

functions on the same coordinate plane

Answer 1

A graph of each of the transformed linear function, g(x) and the parent function, f(x) is shown on the coordinate plane in the picture below.

Part 1.

Since the transformed linear function is g(x) = f(x) + 4, we can logically deduce that the parent function f(x) = x was vertically shifted up by 4 units as follows;

f(x) = x

g(x) = f(x) + 4

g(x) = x + 4

Part 2.

Since the transformed linear function is g(x) = -f(x), we can logically deduce that the parent function f(x) = x was vertically compressed by a factor of 1/3 as follows;

f(x) = x

g(x) = 1/3(f(x))

g(x) = 1/3(x)

Part 3.

Since the transformed linear function is g(x) = -f(x), we can logically deduce that the parent function f(x) = x was reflected across the x-axis as follows;

f(x) = x

g(x) = -f(x)

g(x) = -x

Part 4.

Since the transformed linear function is g(x) = -f(x), we can logically deduce that the parent function f(x) = x was vertically stretched by a factor of 3 as follows;

f(x) = x

g(x) = 3f(x)

g(x) = 3x