Question

Can Somebody Please Help With This?

Answer 1

Answer:

Following is the conclusion and matching each tile with answer:

A. vertical stretch of a factor of 3                   →  g ( x ) = 3 (5)ˣ

B. vertical compression of a factor of 1/3      →  g ( x ) = 1/3 (5)ˣ

C. horizontal stretch of a factor of 3              →  $g(x) = 5^{\frac{1}{3}x}$

D. horizontal compression of a factor of 1/3  →  $g(x) = 5^{3x}$

Step-by-step explanation:

let us suppose a function f ( x ), and a new function g ( x ) = a f ( x )

When a function is multiplied by a positive constant, let say 'a', you normally get a function the graph of which is vertically compressed or stretched with respect to the graph of the original function.

• If the value of constant 'a' is greater than 1, the graph is vertically stretched.
• If the value of constant 'a' is greater than 0 but lesser than 1, the graph will be vertically compressed.

So, the function g ( x ) = 1/3 (5)ˣ is compressed vertically by 1/3, as the multiplied value of constant 'a' = 1/3 is less than 1.

And, the function g ( x ) = 3 (5)ˣ is stretched vertically by 3, as the multiplied value of constant 'a' = 3 is greater than 1.

Now, let us suppose a function f ( x ), and a new function g ( x ) =  f ( bx )

Observe the certain changes right inside the function. In other words, when the input of a function is multiplied by a positive constant, let say 'b', we get a function the graph of which is horizontally compressed or stretched.

• If the value of constant 'b' is greater than 1, the graph is horizontally compressed by a factor of 1/b.
• If the value of constant 'b' is greater than 0 but lesser than 1, the graph will be horizontally stretched 1/b.

So, the graph $g(x) = 5^{\frac{1}{3}x}$  is horizontally stretched by 3, as the value of constant 'b' is greater than 0 but lesser than 1.

And, the graph $g(x) = 5^{3x}$ is horizontally compressed by 1/3, as the value of constant 'b' is greater than 1.

Following is the conclusion and matching each tile with answer:

A. vertical stretch of a factor of 3                   →  g ( x ) = 3 (5)ˣ

B. vertical compression of a factor of 1/3      →  g ( x ) = 1/3 (5)ˣ

C. horizontal stretch of a factor of 3              →  $g(x) = 5^{\frac{1}{3}x}$

D. horizontal compression of a factor of 1/3  →  $g(x) = 5^{3x}$

Keywords: vertical stretch, vertical compression, horizontal stretch, horizontal compression

Learn more about vertical stretch, vertical compression, horizontal stretch, horizontal compression from brainly.com/question/11385040

#LearnwithBrainly