Describe how to obtain the graph of f(x)=x+1−−−−−√−2 by transforming the parent graph of f(x) =x√ .

Question 2 options:

Shift the graph two units down and one unit right.

Shift the graph two units up and one unit right.

Shift the graph two units down and left one unit.

Reflect the graph over the x-axis and shift the graph down 2 units.

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parmesanchilliwack parmesanchilliwack · Answer 1 · 2019-02-04T13:30:07+01:00

Answer: Shift the graph two units down and left one unit.

Step-by-step explanation:

Here the parent function,

[tex]f(x) = \sqrt{x}[/tex]

When the function is shifted left by a factor a then the new function is,

[tex]f(x) = \sqrt{x+a}[/tex]

While when the function is shifted right by a factor A then new function,

[tex]f(x) = \sqrt{x-a}[/tex]

Since here the transformed function is, [tex]f(x) = \sqrt{x+1} - 2[/tex]

Therefore it was obtained by shifting 1 unit towards left,

Now, when the parent function is shifted vertically upward by a factor a,

Then the new function is, [tex]f(x) = \sqrt{x}+a[/tex]

While, when the parent function is shifted vertically downward by a factor a,

Then the new function is, [tex]f(x) = \sqrt{x}-a[/tex]

Here, the transformed function is, [tex]f(x) = \sqrt{x+1} - 2[/tex],

Therefore, it was obtained by shifting 2 unit downward.

Hence, Third Option is correct.

adefioyelaoye adefioyelaoye · Answer 2 · 2022-04-01T17:12:14+02:00

The graph can be obtained by shifting it two units down and left one unit.

This is a mathematical diagram which shows the relationship between two or more sets of numbers or measurements.

Here the parent function, f(x) = √x

When the function is shifted left f(x) = √x+a

When the function is shifted right f(x) = √x - a

Transformed function f(x) = √x + 1 - 2

It was obtained by shifting 1 unit towards left.

Function is shifted vertically upward f(x) = √x+a

Function is shifted vertically downward f(x) = √x- a

Transformed function f(x) = √x + 1 - 2

It was obtained by shifting 2 unit downward.

This therefore makes option C the most appropriate choice.

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