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If function [tex]f[/tex] is the parent exponential function [tex]f(x)=e^x[/tex], what is the equation of the transformed function [tex]g[/tex] in terms of function [tex]f[/tex]?

Replace the value of [tex]a[/tex] to complete the equation:
[tex]
g(x)=a f(x)
[/tex]

Sagot :

GinnyAnswer
To determine the equation of the transformed function [tex]\( g \)[/tex] in terms of [tex]\( f(x) \)[/tex], we start with the parent function [tex]\( f(x) = e^x \)[/tex].

Given that the transformation involves multiplying the parent function [tex]\( f(x) \)[/tex] by a scalar [tex]\( a \)[/tex], the equation can be expressed as:

[tex]\[ g(x) = a \cdot f(x) \][/tex]

Since [tex]\( f(x) = e^x \)[/tex], we substitute [tex]\( f(x) \)[/tex] into the above equation:

[tex]\[ g(x) = a \cdot e^x \][/tex]

Thus, the equation for the transformed function [tex]\( g \)[/tex] in terms of [tex]\( f(x) \)[/tex] and the scalar [tex]\( a \)[/tex] is:

[tex]\[ g(x) = a \cdot e^x \][/tex]

This equation represents the transformed function, where [tex]\( a \)[/tex] acts as a scaling factor to the original exponential function [tex]\( f(x) = e^x \)[/tex].
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