Question

Consider the following function :y=1/(x+5)+2 How does the graph of this function compare with the graph of the parent function, y=1/x

Answer 1

With respect to the parent function,
  y = 1/(x+5) +2
is translated 5 units left and 2 units up.

Answer 2

As the given parent function is added 5 units in the variable and 2 units out of the function. Thus, The given parent function is first shifts 5 units left and then 2 units up as shown in the figure below.

What is transformation of a function?

Transformation of a function is shifting the function from its original place in the graph.

Types of transformation-

• Horizontal shift- Let the parent function is $f(x)$. Thus by replacing parent function with $f(x-b)$ shifts the graph b units right and by replacing parent function with $f(x+b)$ shifts the graph b units left.

• Vertical shift- Let the parent function is $f(x)$. Thus by replacing parent function with $f(x)+c$ shifts the graph c units up and by replacing parent function with $f(x)-c$ shifts the graph c units down.

Given information-

The given parent function in the problem is,

$y=\dfrac{1}{x}$

Here the function is first shifts 5 units left and become,

$y=\dfrac{1}{x+5}$

Then the function is shifts 2 units up as,

$y=\dfrac{1}{x+5}+2$

Hence the given parent function is first shifts 5 units left and then 2 units up as shown in the figure below.

Learn more about the transformation of a function here;

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