Please help with the attached question. Thanks

To shift a function on a cartesian plane to the left by [tex]a[/tex] units, add [tex]a[/tex] to its independent variable. Think about how [tex](x-a)[/tex], which is to the left of [tex]x[/tex], will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by [tex]a[/tex] units, subtract [tex]a[/tex] from its independent variable.

For example, [tex]G(x+1)[/tex] is [tex]1[/tex] unit to the left of [tex]G(x)[/tex]. Conversely, [tex]G(x-1)[/tex] is [tex]1[/tex] unit to the right of [tex]G(x)[/tex]. The new function is to the left of [tex]G(x)[/tex]. Meaning that [tex]F(x)[/tex] should should add [tex]1[/tex] to (rather than subtract [tex]1[/tex] from) the independent variable of [tex]G(x)[/tex]. That rules out choice B) and D).

Multiplying a function by a number that is greater than one will stretch its graph vertically.
Multiplying a function by a number that is between zero and one will compress its graph vertically.
Multiplying a function by a number that is between [tex]-1[/tex] and zero will flip its graph about the [tex]x[/tex]-axis. Doing so will also compress the graph vertically.
Multiplying a function by a number that is less than [tex]-1[/tex] will flip its graph about the [tex]x[/tex]-axis. Doing so will also stretch the graph vertically.

The graph of [tex]G(x)[/tex] is stretched vertically. However, similarly to the graph of this graph [tex]G(x)[/tex], the graph of [tex]F(x)[/tex] increases as [tex]x[/tex] increases. In other words, the graph of [tex]G(x)[/tex] isn't flipped about the [tex]x[/tex]-axis. [tex]G(x)[/tex] should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points [tex](x, y)[/tex]'s that are on the graph of [tex]F(x)[/tex] fit into the expression [tex]y = F(x) = 3\sqrt{x - 1}[/tex].

wegnerkolmp2741o wegnerkolmp2741o · Answer 2 · 2019-07-06T02:17:36+02:00

Answer:

f(x) =3 sqrt(x+1)

Step-by-step explanation:

We notice two things about the graph, it has a shift to the left and is steeper

First the shift to the left

f(x) = g(x + C)

C > 0 moves it left

C < 0 moves it right

g(x) is 0 at x=0 f(x) is 0 at x=-1

We are moving it 1 unit to the left

This means our "c" is 1

f(x) = sqrt( x+1)

Now we need to deal with the graph getting steeper

f(x) = Cg(x)

C > 1 stretches it in the y-direction

0 < C < 1 compresses it

Since it is getting taller, "c" must be greater than 1

Remember the - sign means it is a reflection across the x axis, which we do not have

f(x) =3 sqrt(x+1)