Answer:
The resulting expression is [tex]g(x) = \frac{1}{13}\cdot 2^{x+3}+3[/tex]. 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 [tex]f(x) = 2^{x}[/tex], each operation is defined below:
Vertical compression
[tex]g(x) = k\cdot f(x)[/tex], where [tex]0 < k < 1[/tex]. (1)
Vertical translation upwards
[tex]g(x) = f(x) + c[/tex], where [tex]c > 0[/tex]. (2)
Horizontal translation leftwards
[tex]g(x) = f(x+b)[/tex], [tex]b > 0[/tex]. (3)
Now, we proceed to transform the parent exponential function:
(i) A vertical compression by a scale factor of 13 ([tex]k = \frac{1}{13}[/tex])
[tex]f'(x) = \frac{1}{13}\cdot 2^{x}[/tex]
(ii) Vertical translation of 3 units up
[tex]f'' (x) = \frac{1}{13}\cdot 2^{x} + 3[/tex]
(iii) Horizontal translation of 3 units to the left
[tex]g(x) = \frac{1}{13}\cdot 2^{x+3}+3[/tex]
The resulting expression is [tex]g(x) = \frac{1}{13}\cdot 2^{x+3}+3[/tex]. We include the graph of both functions, the red line represents the parent exponential function, whereas the blue line is for the resulting function.
