Methods2025 Exam 2 Section A · Q20CAS active1 mark

Transformations of an exponential function

Let $a > 1$ , and consider the functions $f$ and $g$ defined below.

$f : R \to R,\ f(x) = a^x$

$g : R \to R,\ g(x) = a^{2x+2}$

Which one of the following sequences of transformations, when applied to $f(x)$ , does not produce $g(x)$ ?

1 mark

Adilation by a factor of

\frac{1}{2}

from the

y

-axis, then translation by 1 unit in the negative direction of the

x

-axisBdilation by a factor of

\frac{1}{2}

from the

y

-axis, then dilation by a factor of

a^2

from the

x

-axisCdilation by a factor of

a

from the

x

-axis, then dilation by a factor of

\frac{1}{2}

from the

y

-axis, then translation by 1 unit in the positive direction of the

x

-axisDdilation by a factor of

a^3

from the

x

-axis, then translation by 1 unit in the positive direction of the

x

-axis, then dilation by a factor of

\frac{1}{2}

from the

y

-axis

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