Answer:
<em>The matched table:</em>
<em>A. vertical stretch of a factor of 3 ⇒ g ( x ) = 3 (5)ˣ</em>
<em>B. vertical compression of a factor of 1/3 ⇒ g ( x ) = 1/3 (5)ˣ</em>
<em>C. horizontal stretch of a factor of 3 ⇒ </em>
<em>D. horizontal compression of a factor of 1/3 ⇒ </em>
Step-by-step explanation:
IDENTIFYING VERTICAL STRETCH AND COMPRESSION
Let us consider the given function f(x) = <em>5ˣ</em>
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) = <em>5ˣ</em>
<em>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.</em>
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 <em> would be horizontally stretched by 3. The reason is simple. The constant value 1/3 is greater than 0 but lesser than 1.</em>
<em>And the function would be</em> stretched vertically by 3. <em>The reason is simple. The constant value 3 </em>is greater than 1.
So, the correct box would look like this:
<em>A. vertical stretch of a factor of 3 ⇒ g ( x ) = 3 (5)ˣ</em>
<em>B. vertical compression of a factor of 1/3 ⇒ g ( x ) = 1/3 (5)ˣ</em>
<em>C. horizontal stretch of a factor of 3 ⇒ </em>
<em>D. horizontal compression of a factor of 1/3 ⇒ </em>
<em>Keywords: transformation, horizontal stretch and compression, vertical stretch and compression</em>
<em>Learn more about </em>horizontal stretch and compression<em>, </em>vertical stretch and compression <em>from brainly.com/question/1806691</em>
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