Answer:
C. 7
Step-by-step explanation:
We have been given graphs of two exponential functions, f and g.
[tex]g(x)=f(x)+k[/tex]
We can see that our parent function f(x) is translated k units to get function g(x).
The rules for translation are mentioned below.
Horizontal shifting:
[tex]f(x-a)[/tex]= Graph shifted to right by a units.
[tex]f(x+a)[/tex]= Graph shifted to left by a units.
Vertical shifting:
[tex]f(x)+a[/tex]= Graph shifted upwards by a units.
[tex]f(x)-a[/tex]= Graph shifted downwards by a units.
Upon comparing our given graph with transformation rules we can see that our function f(x) is translated k units upward to get function g(x).
Now let us find the value of k from our given graph.
We can see that initial value (y-intercept) of f(x) is -4 and initial value of g(x) is 3. Difference between y-intercepts of both functions is 7.
[tex]\text{Difference between y-intercepts}= 3--4=3+4=7[/tex]
Our parent function f(x) is shifted 7 units upwards to get new function g(x), therefore the value of k is 7 and option C is the correct choice.
