Answer:
When we multiply the exponential function [tex]f(x) = 2^{\frac{1}{2}x[/tex] with 3. As 3 > 0. So, it means the graph would be vertically stretched by a factor 3. So, the resulting graph [tex]f(x) = 3.2^{\frac{1}{2}x[/tex] is obtained after a vertical stretch of [tex]f(x) = 2^{\frac{1}{2}x[/tex] by 3 factor. Please check the figure a and b.
Step-by-step explanation:
Let us suppose the parent exponential function
[tex]f(x) = 2^{\frac{1}{2}x[/tex]
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 [tex]f(x) = 2^{\frac{1}{2}x[/tex] as shown in figure a.
So, when we multiply the exponential function [tex]f(x) = 2^{\frac{1}{2}x[/tex] with 3. As 3 > 0. So, it means the graph would be vertically stretched by a factor 3. So, the resulting graph [tex]f(x) = 3.2^{\frac{1}{2}x[/tex] is obtained after a vertical stretch of [tex]f(x) = 2^{\frac{1}{2}x[/tex] by 3 factor.
Check the attached figure b to visualize the comparison of [tex]f(x) = 2^{\frac{1}{2}x[/tex] and the resulting graph [tex]f(x) = 3.2^{\frac{1}{2}x[/tex].
It is clear from the comparison as shown in figure b, that when we multiplied the exponential function [tex]f(x) = 2^{\frac{1}{2}x[/tex] with 3, graph would be vertically stretched by a factor 3.
Keywords: vertically stretch, exponential function
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