Question

Describe the transformations made on this function:(stretch/compression, reflect, left/right, up/down)

Answer 1

The function we have is:

$f(x)=\frac{1}{2}(x-7)^3+6$

Since this is a cubic function, we start with the parent cubic function (the simplest form of the cubic function):

$f(x)=x^3$

And compare it to the given function.

The first thing we can note is that there was a subtraction of 7 to the value of x:

$x\longrightarrow x-7$

When we add a number to the x value, the graph moves to the left, and when we subtract a number to the x value, the graph moves to the right.

So the first transformation is moving to the right 7 units.

Next, we have that there was +6 added to the expression --> When you add a number to the function, the graph moves up, and when you subtract a number to the function, the graph moves down.

In this case, since we added a constant value of 6, the graph is translated 6 units up.

The second transformation is moving up 6 units.

Finally, let's analyze the effect that the 1/2 has on the function.

We can compress or stretch the graph of a function by multiplying the x by a constant (a number). If the number of between 0 and 1, there is a stretch, and if the number is greater than 1 there is compression.

In this case, the number next to the x is:

$\frac{1}{2}=0.5$

Since the number is between 0 and 1 there is a stretch of the function.

In summary:

Answer:

Translation of 7 units to the right

Translation of 6 units up

Stretch of the function of 0.5