Question

. Your friend attempted to describe the transformations applied to the graph of f(x)=\sqrt{x} to give the equation g(x)=2\sqrt{-3(x+3)}-1. They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.

a) f(x) has been reflected vertically.
b) f(x) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has been translated left 3 units.
e) f(x) has been translated up 1 unit.

help me please

Answer 1

Answer:

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Answer 2

$f(x)=\sqrt{x}$ and $g(x)=2\sqrt{-3(x+3)} -1$

Step-by-step explanation:

To describe the transformation, compare the given equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

The transformation from the first equation to the second one can be found by finding $a$, $h$ and $k$ from $y=a\sqrt{x-h} +k$.

• The horizontal shift depends on the value of $h$.
• $h>0$ is a shift to right and $h<0$ is a shift to left.
• The vertical shift depends on the value of $k$.
• $k>0$ is a shift upwards and $k<0$ is a shift downwards.
• The value of $a$ describes the vertical stretch or compression of the graph.
• $a>1$ is a vertical stretch and $0<a<1$ is a vertical compression.
• The sign of $a$   describes the reflection across the x-axis.  $-a$ means the graph is reflected across the x-axis.

The parent equation is, $f(x)=\sqrt{x}$

The transformation is given by, $g(x)=2\sqrt{-3(x+3)} -1$

Here, $k=-1$.

That means, $f(x)$ has been translated $1$ units down.

$h=-3$.

That means, $f(x)$ has been translated $3$ units left.

And, $a=2$

That means, $f(x)$ has been stretched vertically by a factor of $2$.

Also, $a$ is positive. So, there is no reflection across the x-axis.

Therefore, we can say that

Options $(b)$ and $(d)$ are identified correctly.

Options $(a),(c)$ and $(e)$ are not identified correctly.