Question

Which function represents a vertical stretch of an exponential function? f (x) = 3 (one-half) Superscript x f (x) = one-half (3) Superscript x f (x) = (3) Superscript 2 x f (x) = 3 Superscript (one-half x)

Answer 1

Answer:

When we multiply the exponential function $f(x) = 2^{\frac{1}{2}x$ with 3. As 3 > 0. So, it means the graph would be vertically stretched by a factor 3. So, the resulting graph $f(x) = 3.2^{\frac{1}{2}x$ is obtained after a vertical stretch of $f(x) = 2^{\frac{1}{2}x$ by 3 factor. Please check the figure a and b.

Step-by-step explanation:

Let us suppose the parent exponential function

$f(x) = 2^{\frac{1}{2}x$

The rule of vertical stretch of an exponential function states that when we multiply the parent function by a constant, let suppose 'c', then the value of c must be greater than 0. i.e. |c| > 0. And the graph would be vertically stretched by a factor c.

For example, let suppose the parent exponential function is $f(x) = 2^{\frac{1}{2}x$ as shown in figure a.

So, when we multiply the exponential function $f(x) = 2^{\frac{1}{2}x$ with 3. As 3 > 0. So, it means the graph would be vertically stretched by a factor 3. So, the resulting graph $f(x) = 3.2^{\frac{1}{2}x$ is obtained after a vertical stretch of $f(x) = 2^{\frac{1}{2}x$ by 3 factor.

Check the attached figure b to visualize the comparison of $f(x) = 2^{\frac{1}{2}x$ and the resulting graph $f(x) = 3.2^{\frac{1}{2}x$.

It is clear from the comparison as shown in figure b, that when we multiplied the  exponential function $f(x) = 2^{\frac{1}{2}x$ with 3, graph would be vertically stretched by a factor 3.

Keywords: vertically stretch, exponential function

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Answer 2

Answer:

f(x) = 3$(\frac{1}{2})^{x}$

Step-by-step explanation:

hope it helps!