Question

Consider the function f(x) = x(x-4.

If the point (2+c,y) is on the graph of f(x), the following point will also be on the graph of f(x):
A) (c-2,y)
B) (2-c,y)

Answer 1

Explanation:

point (c-2, y) lies on the graph of f(x)=x(x-4)f(x)=x(x−4) .

Explanation:

Given function f(x)=x(x-4)f(x)=x(x−4) also point (2+ c,y) is on the graph of f(x) ,

We have to find out of given point which point will also be on the graph of f(x).

Consider the given function f(x)=x(x-4)f(x)=x(x−4)

f(x)=x(x-4)f(x)=x(x−4) can be rewritten f(x)=x^2-4xf(x)=x

2

−4x

Now we substitute the given point (2+ c, y) in the function given ,

we have,

f(x)=y=x(x-4)f(x)=y=x(x−4)

put for x as 2+c , we have,

\Rightarrow y=(2+c)(2+c-4)⇒y=(2+c)(2+c−4)

Solve, we get

\Rightarrow y=(2+c)(c-2)⇒y=(2+c)(c−2)

Thus, both point (2+c, y) and (c-2, y) lies on the graph of f(x)=x(x-4)f(x)=x(x−4)

Thus, option (1) is correct.