Question

The parent exponential function of f(x)=2x has been transformed in the following ways:

Answer 1

Answer:

The resulting expression is $g(x) = \frac{1}{13}\cdot 2^{x+3}+3$. We include the graph of both functions, the red line represents the parent exponential function, whereas the blue line is for the resulting function.

Step-by-step explanation:

Statement is incomplete. The question is missing. We infer that question is: What is the resulting expression? Let $f(x) = 2^{x}$, each operation is defined below:

Vertical compression

$g(x) = k\cdot f(x)$, where $0 < k < 1$. (1)

Vertical translation upwards

$g(x) = f(x) + c$, where $c > 0$. (2)

Horizontal translation leftwards

$g(x) = f(x+b)$, $b > 0$. (3)

Now, we proceed to transform the parent exponential function:

(i) A vertical compression by a scale factor of 13 ($k = \frac{1}{13}$)

$f'(x) = \frac{1}{13}\cdot 2^{x}$

(ii) Vertical translation of 3 units up

$f'' (x) = \frac{1}{13}\cdot 2^{x} + 3$

(iii) Horizontal translation of 3 units to the left

$g(x) = \frac{1}{13}\cdot 2^{x+3}+3$

The resulting expression is $g(x) = \frac{1}{13}\cdot 2^{x+3}+3$. We include the graph of both functions, the red line represents the parent exponential function, whereas the blue line is for the resulting function.