Question

DRAG EACH tile to the correct box.


Consider this function.

f(x) = 5^x


How is function f transformed to create function g?


Match each transformation of function f with its description.


A. vertical stretch of a factor of 3


B. vertical compression of a factor of 1/3


C. horizontal stretch of a factor of 3


D. horizontal compression of a factor of 1/3


Options:

1. g(x) = 3(5)^x

2. g(x) = 1/3(5)^x

3. g(x) = 5^1/3x

4. g(x) = 5^3x

Answer 1

Answer:

The matched table:

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:

IDENTIFYING VERTICAL STRETCH AND COMPRESSION

Let us consider the given function f(x) = 5ˣ

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

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

IDENTIFYING HORIZONTAL STRETCH AND COMPRESSION

Let us consider the given function f(x) = 5ˣ

Note: please remember that when the function input gets multiplied by a positive constant - assuming that constant as 'b' - we would obtain a function - a transformed function with a graph horizontally compressed or stretched.

If b > 1, the graph would be horizontally compressed by a factor of 1/b.

If 0 < b < 1, the graph would be horizontally stretched 1/b.

So the function $g(x) = 5^{\frac{1}{3}x}$ would be horizontally stretched by 3. The reason is simple. The constant value 1/3 is greater than 0 but lesser than 1.

And the function $g(x) = 5^{3x}$ would be stretched vertically by 3. The reason is simple. The constant value 3 is greater than 1.

So, the correct box would look like this:

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: transformation, horizontal stretch and compression, vertical stretch and compression

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Answer 2

Answer:

The answer is:

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

horizontal stretch of a factor of 3 = g(x)=5^1/3x

horizontal compression of a factor of 1/3 = g(x)=5^3x

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

Step-by-step explanation:

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