Question

Which statement is true regarding the functions on the graph?
f(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)

Answer 1

Here looking at the graphs we can see that two functions $f(x)$ and $g(x)$  are plotted on the coordinate plane.

Now, from the graph we can see that $f(x)$ and $g(x)$ intersect at point $(3,6)$.

We can see that the value of the function $f(x)$ at $x=3$ is equal to 6 that is $f(3)=6$.

And the value of the function $g(x)$ at $x=3$ is also equal to 6 that is $g(3)=6$.

Both the functions are equal at $x=3$.

Therefore, it can be concluded that $f(3)=g(3)=6$.

So the correct statement is $f(3)=g(3)$.

Answer 2

The statement that is true regarding the considered graph is given by: Option B: f(3) = g(3)

How do we make graph of a function?

Suppose the considered function whose graph is to be made is $f(x)$

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values $f(x)$ are plotted on the vertical axis.

They are together plotted on the point $(x,y) = (x, f(x))$

This is why we usually write the functions as: $y = f(x)$

For this case, on the value of x = 3, the functions f(x) and g(x) both have same output 6. This is why they are intersecting each other, as their respective points $\rm (3,f(3)), \: \rm and \: (3, g(3))$ of the graph coincide.

We have

$f(3) = 6\\g(3) = 6$

Thus, we have:  f(3) = g(3) = 6

Therefore, the statement that is true regarding the considered graph is given by: Option B: f(3) = g(3)

Learn more about graphing functions here:

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