Question

A function f is given, and the indicated transformations are applied to its graph (in the given order).

Write the equation for the final transformed graph.
11. f(x) = x³: shift leff 1. stretch vertically by a factor of 3. shift up 1

Answer 1

g(x) = 3(x + 1)³ + 1

Explanation:

To write the equation for the final transformed graph, we need to apply the indicated transformations in the given order to the original function f(x) = x³.

The transformations are:

1. Shift left 1 unit.
2. Stretch vertically by a factor of 3.
3. Shift up 1 unit.

1. Shift left 1 unit

To shift the graph to the left by one unit, we add one to the x-variable, so replace x with (x + 1). Therefore, the new function after the first transformation is:

g(x) = (x + 1)³

2. Stretch vertically by a factor of 3

To stretch the graph vertically by a factor of 3, we multiply the function by 3. So, the new function after the second transformation is:

g(x) = 3(x + 1)³

3. Shift up 1 unit

To shift the graph up by 1 unit, we add 1 to the function. So, the final function after the third transformation is:

g(x) = 3(x + 1)³ + 1