Question

Given that the point (8, 3) lies on the graph of g(x) = log2x, which point lies on the graph of f(x) = log2(x + 3) + 2?

Answer 1

The answer to this one is 5, 5 on edg

Answer 2

The point lies on the graph of $f(x) = log2(x + 3) + 2$ will lie on $(5,5)$ .

What is graph ?

Graph is

And the parent quadratic function is in the form of $f(x)=a(x-h)^2+k$,

Here,

"$h$" tells if the vertex of the parabola is going left or right.

"$k$" determines if the vertex of the parabola is going up or down.

We have,

$g(x) = log2x$

And,  point $(8, 3)$ which lies on the graph of $g(x) = log2x$,

And,

$f(x) = log2(x + 3) + 2$

And,  point $(8x,y)$ which lies on the graph of $f(x) = log2(x + 3) + 2$.

Now,

Compare $f(x)$ and $g(x)$ ,

$g(x) = log2x$

$f(x) = log2(x + 3) + 2$

We can see that,

There is a addition of $3$ to $x$ which means $h=3$ and horizontal shift towards left so, point will also be shifted $3$ units to left (because original equation has negative sign ).

i.e. $(8-3)=5$

And

here is a addition of $2$ to the whole function which means $k=2$ i.e. vertical shift upwards by $2$ units so, the point will also be shifted $2$ units up (because we positive sign in main equation so adding means going upward).

i.e. $3+2=5$

So, the points of $f(x) = log2(x + 3) + 2$ are $(5,5)$ .

Hence, we can say that the point lies on the graph of $f(x) = log2(x + 3) + 2$ will lie on $(5,5)$ .

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