Question

Pls help

A function f(x)=\sqrt(x) is transformed into function g(x)=3\sqrt(x-2)+5

Name the 3 transformations that occurred and describe the general shape of g(x). When describing the shape, you have the option of including a picture of its graph.

Answer 1

`g(x)=\sqrt[3]{x-3}`

Answer 2

Explanation:

The parent function is the simplest form of the type of function given.

f(x)=√x

The transformation from the first equation to the second one can be found by finding a

, h, and k

for each equation.

y=a√x−h+k

Factor a 1

out of the absolute value to make the coefficient of x equal to 1

.

y=√x

Factor a 1

out of the absolute value to make the coefficient of x equal to 1

.

y=√x−3+2

Find a

, h, and k for y=√x−3+2

.

a=1

h=3

k=2

The horizontal shift depends on the value of h

. When h>0

, the horizontal shift is described as:

g(x)=f(x+h)

- The graph is shifted to the left h

units.

g(x)=f(x−h)

- The graph is shifted to the right h

units.

Horizontal Shift: Right 3

Units

The vertical shift depends on the value of k

. When k>0

, the vertical shift is described as:

g(x)=f(x)+k

- The graph is shifted up k

units.

g(x)=f(x)−k

- The graph is shifted down k

units.

Vertical Shift: Up 2

Units

The sign of a

describes the reflection across the x-axis. −a

means the graph is reflected across the x-axis.

Reflection about the x-axis: None

The value of a

describes the vertical stretch or compression of the graph.

a>1

is a vertical stretch (makes it narrower)

0<a<1

is a vertical compression (makes it wider)

Vertical Compression or Stretch: None

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function: f(x)=√x

Horizontal Shift: Right 3

Units

Vertical Shift: Up 2

Units

Reflection about the x-axis: None

Vertical Compression or Stretch: None