Question

What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x − 6)

Answer 1

Answer:

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$.

Step-by-step explanation:

When we Add or subtract a positive constant, let say c, to input x, it would be a horizontal shift.  

For example:

Type of change               Effect on y = f(x)

$y = f(x - c)$                      horizontal shift: c units to right

So

Considering the function

$f(x) = x^2$

The graph is shown below. The first figure is representing $f(x) = x^2$.

Now, considering the function

$\:f\left(x\right)=\left(x-6\right)^2$

According to the rule, as we have discussed above, as a positive constant 6 is added to the input, so there is a horizontal shift, 6 units to the right.

The graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shown below in second figure. It is clear that the graph of  $\:f\left(x-6\right)=\left(x-6\right)^2$  is shifted 6 units to the right as compare to the function $f(x) = x^2$.

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$.