Question

The graph of y = 3/x is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?

Answer 1

Answer: The required equation of f(x) is $f(x)=-\frac{3}{x} -2$.

Explanation:

The given equation is,

$y=\frac{3}{x}$

If the graph reflects across the y-axis then,

$(x,y)\rightarrow (-x,y)$

It means the y coordinate is same and the sign x coordinate changed.

So, the equation of given graph after reflection across the y axis is,

$y_1=\frac{3}{-x}$

After reflection the graph shifts 2 unit down.

If a graph translate 2 unit down then,

$(x,y)\rightarrow (x,y-2)$

So, the function f(x) is,

$f(x)=y_1-2$

$f(x)=\frac{3}{-x}-2$

$f(x)=-\frac{3}{x}-2$

Therefore the equation of f(x) is $f(x)=-\frac{3}{x} -2$.

Answer 2

The equation of the graph of f(x) is $f(x) - \frac 3x - 2$

The equation of the function is given as:

$y= \frac 3x$

The rule of reflecting the function over the y-axis is:

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

So, we have:

$y= -\frac 3x$

The rule of translating the function down by 2 units is:

$(x,y) \to (x,y-2)$

So, we have:

$f(x) - \frac 3x - 2$

Hence, the graph of f(x) is $f(x) - \frac 3x - 2$

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