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Consider the graph of the function [tex]f(x) = e^x[/tex].

What is the [tex]y[/tex]-intercept of the function [tex]g[/tex] if [tex]g(x) = 2f(x) + 1[/tex]?

A. [tex]\((0, 1)\)[/tex]
B. [tex]\((0, 3)\)[/tex]
C. [tex]\((0, -1)\)[/tex]
D. [tex]\((0, 2)\)[/tex]

Sagot :

GinnyAnswer
To find the [tex]\( y \)[/tex]-intercept of the function [tex]\( g(x) = 2f(x) + 1 \)[/tex], where [tex]\( f(x) = e^x \)[/tex], we need to determine the value of [tex]\( g(x) \)[/tex] when [tex]\( x = 0 \)[/tex].

First, substitute [tex]\( x = 0 \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]\[ f(0) = e^0 \][/tex]

Since [tex]\( e^0 = 1 \)[/tex]:
[tex]\[ f(0) = 1 \][/tex]

Next, substitute [tex]\( f(0) \)[/tex] into [tex]\( g(x) \)[/tex]:
[tex]\[ g(0) = 2f(0) + 1 \][/tex]
[tex]\[ g(0) = 2 \cdot 1 + 1 \][/tex]
[tex]\[ g(0) = 2 + 1 \][/tex]
[tex]\[ g(0) = 3 \][/tex]

Therefore, the [tex]\( y \)[/tex]-intercept of the function [tex]\( g(x) \)[/tex] is [tex]\( (0, 3) \)[/tex].

The correct answer is:

B. [tex]\((0, 3)\)[/tex]
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