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Consider the functions
g and
h given by
g(x)=4^(x) and
h(x)=16^(x+2). In the
xy-plane, what is the
x-coordinate of the point of intersection of the graphs of
g and
h ?
(A) -4
(B) -2
(C) 0
(D) 2

$\newline$ Consider the functions $g$ and $h$ given by $g(x)=4^{x}$ and $h(x)=16^{x+2}$ . In the $x y$ -plane, what is the $x$ -coordinate of the point of intersection of the graphs of $g$ and $h$ ? $\newline$ (A) $-4$ $\newline$ (B) $-2$ $\newline$ (C) $0$ $\newline$ (D) $2$

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Transformations of quadratic functions

Full solution

Q.

\newline

Consider the functions

g

and

h

given by

g(x)=4^{x}

and

h(x)=16^{x+2}

. In the

x y

-plane, what is the

x

-coordinate of the point of intersection of the graphs of

g

and

h

?

\newline

(A)

-4

\newline

(B)

-2

\newline

(C)

0

\newline

(D)

2

Set $g(x)$ equal: Set $g(x)$ equal to $h(x)$ to find the $x$ -coordinate of the intersection point. $\newline$ $g(x) = h(x)$ $\newline$ $4^x = 16^{(x+2)}$
Recognize base relationship: Recognize that $16$ is $4$ squared ( $4^2$ ). $\newline$ $4^x = (4^2)^{(x+2)}$
Apply power rule: Apply the power of a power rule: $(a^b)^c = a^{(b*c)}$ . $4^x = 4^{2*(x+2)}$
Set exponents equal: Since the bases are the same, set the exponents equal to each other. $x = 2*(x+2)$
Distribute and simplify: Distribute the $2$ on the right side of the equation. $x = 2x + 4$
Subtract to solve: Subtract $2x$ from both sides to solve for $x$ . $\newline$ $x - 2x = 4$
Combine like terms: Combine like terms. $\newline$ $-1x = 4$

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