Question

How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) = StartFraction 1 Over x EndFraction?
g(x) is shifted 4 units right and 6 units up from f(x).
g(x) is shifted 4 units right and 6 units down from f(x).
g(x) is shifted 4 units left and 6 units up from f(x).
g(x) is shifted 4 units left and 6 units down from f(x).

Answer 1

Answer:

Option D.

Step-by-step explanation:

The given parent function is

$f(x)=\dfrac{1}{x}$

The given function is

$g(x)=\dfrac{1}{x+4}-6$

Using the parent function, the given function can be written as

$g(x)=f(x+4)-6$        ...(1)

The translation is defined as

$g(x)=f(x+a)+b$        .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

$a=4>0$, it means the graph shifts 4 units left.

$b=-6<0$, it means the graph shifts 6 units down.

So, g(x) is shifted 4 units left and 6 units down from f(x).

Therefore, the correct option is D.

Answer 2

Transformation involves changing the form of a function.

The true option is (d) g(x) is shifted 4 units left and 6 units down from f(x).

The functions are given as:

$g(x)= \frac{1}{x + 4} - 6$

$f(x)= \frac{1}{x}$

Start by shifting the function to the left, by 4 units.

This is represented as:

$(x,y) \to (x + 4,y)$

So, we have:

$f'(x)= \frac{1}{x + 4}$

Next, shift the function down, by 6 units.

This is represented as:

$(x,y) \to (x,y - 6)$

So, we have:

$g(x)= \frac{1}{x + 4} - 6$

Hence, the true option is (d)

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