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When graphed in the
xy-plane, the function
f(x)=3(2)^(x)+1 has a
y-intercept at
(0,k). What is the value of
k ?
Choose 1 answer:
(A) 1
(B) 2
(C) 3
(D) 4

When graphed in the $xy$ -plane, the function $f(x)=3(2)^{x}+1$ has a $y$ -intercept at $(0,k)$ . What is the value of $k$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $2$ $\newline$ (C) $3$ $\newline$ (D) $4$

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Transformations of quadratic functions

Full solution

Q. When graphed in the

xy

-plane, the function

f(x)=3(2)^{x}+1

has a

y

-intercept at

(0,k)

. What is the value of

k

?

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

2

\newline

(C)

3

\newline

(D)

4

Evaluate at $x = 0$ : To find the y-intercept of the function, we need to evaluate the function at $x = 0$ . The y-intercept occurs where the graph of the function crosses the y-axis, which is when $x = 0$ .
Substitute $x = 0$ : Substitute $x = 0$ into the function $f(x) = 3(2)^x + 1$ to find the value of $k$ . $\newline$ $f(0) = 3(2)^0 + 1$
Calculate $2^0$ : Calculate the value of $2$ raised to the power of $0$ , which is $1$ . $\newline$ $2^0 = 1$
Multiply by $3$ : Multiply $3$ by the result from the previous step. $\newline$ $3 \times 1 = 3$
Add $1$ : Add $1$ to the result from the previous step to find the value of $k$ . $\newline$ $3 + 1 = 4$

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